One of the few things we know with certainty about any text is that we started with autographs and ended up with the manuscripts we currently have. Along the way, something happened.
To properly perform textual criticism, we have to try to reconstruct what that "something" was. What we do from there varies, of course; we might select a copy text, or decide to be highly eclectic, or do almost anything else. But, ultimately, every textual process involving two or more manuscripts involves an examination of the history of readings. When we set out to reconstruct the text, we call this the process of examining Internal Evidence.
In assessing these readings, critics evaluate the history of a passage in light of Inherent or Intrinsic Probability and of Transmissional or Transcriptional Probability.
To put this in a single sentence, Inherent Probability concerns itself with what the author is most likely to have written (or what a particular critic thinks the author is most likely to have written), while Transcriptional Probability studies what a scribe might have done to that reading.
Intrinsic Probability is what reading, standing all by itself, makes the most sense. Hort, in §25 of his Introduction, lists factors which might be considered in determining intrinsic probability: "conformity to grammar and congruity to the purport of the rest of the sentence and the larger context; to which may rightly be added congruity to the usual style of the author and to his matter in other passages."
To put that in something more like English, Intrinsic Probability looks at what the author is saying at a particular point, and tries to make sense of the variant in that context; it also looks at the author's style and outlook, and tries looks for the reading which is more typical of the way the author thinks and writes.
To take an example of the latter, there are three instances in Matthew
(11:15, 13:9, 13:43) of variants on the phrase
o ecwn wta [add/omit akouein] akouetw, "let the one who has ears [to hear] hear!"
The usage with akouein is typical of Mark. Matthew is much more concise, and appears in at least two of the cases to have intended the reading o ecwn wta akouetw, lacking the infinitive. So intrinsic probability argues that the shorter reading is the original.
Which brings us to Transcriptional Probability. This is what scribes are likely to have done to a particular reading.
It is interesting to note that Hort spend only three sections on intrinsic probability, but devotes ten (§28-37) to transcriptional probability. After all, he notes (§28) "If one various reading appears to ourselves to give much better sense or in some way to excel another, the same apparent superiority may have led to the introduction of the reading in the first instance. Mere blunders apart, no motive can be thought of which could lead a scribe to introduce a consciously worse reading in place of a better." This leads Hort to the at-first unlikely conclusion, "We might thus seem to be landed in the paradoxical result that intrinsic inferiority is evidence of originality."
But this is not what Hort means. He explains, (§28) "Transcriptional probability is not directly or properly concerned with the relative excellence of rival readings, but merely with the relative fitness of each for explaining the existence of the others. Each rival reading contributes an element to the problem which has to be solved; for every rival reading is a fact which has to be accounted for, and no acceptance of any one reading as original can be satisfactory which leaves any other variant incapable of being traced to some known cause or variation."
Hort's suggested method, then, is to take each of the various readings, assume it is original, and see what happens -- almost a mathematical proposition.
Let's take another Biblical example -- one I've used elsewhere, but a good starting point because there are three readings, which often makes the direction of the changes clearer. The passage is James 5:7, where the Textus Receptus reads o gewrgos ekdecetai ... ewsan labe ueton prwimon kai oyumon, the farmer waits... until he recieves the early and late rain. There are several minor variants in this verse, but the major one is about what the farmer recieves: does he receive ueton, rain; or karpon, fruit; or does the verb lack an object?
The manuscript support is as follows:
All three have early support, and at this stage we are not considering the value of the manuscripts (indeed, it is by assessing readings like this that we determine the value of manuscripts). Assume each reading is original. Start with rain. If it had been original, it could perhaps have been lost by accident. But why change it to fruit? This change makes no sense unless we assume a secondary change: if rain had been lost, a scribe might be tempted to supply an object, and thought of the wrong one.
A similar line of logic applies if we assume fruit is original: To account for all the readings, we must assume a two-stage change: First fruit is dropped, then some scribe emends by adding the object rain.
But assume the original had no object. This is is as awkward in Greek as in English. The temptation would be to add an object. One corrector thought of fruit, a reading which did not survive well; another (perhaps more than one) thought of rain, which is even more suitable and survived well.
Thus, transcriptional probability clearly favors the reading without an object. We adopt it as the original reading -- and we slightly raise our estimate of the manuscripts containing it, for reference in the many cases where transcriptional probability is not so clear.
In deciding how to weigh these sorts of probability, we again turn to Hort, who popularized the terms. Of Intrinsic Probability, he says in §25-27, "The first impulse in dealing with a variation is usually to lean upon Intrinsic Probability, that is, to consider which of two readings makes the best sense, and to decide between them accordingly.... But the uncertainty of the decision in ordinary cases is shown by the great diversity of judgement which is actually found to exist.... [In] dealing with this kind of evidence equally competent critics often arrive at contradictory conclusions as to the same variations. Nor indeed are the assumptions involved in Intrinsic Evidence of Readings to be implicitly trusted. There is much literature, ancient no less than modern, in which it is needful to remember that the authors are not always grammatical, or clear, or consistent, or felicitous.... [In] the highest literature, and notably in the Bible, all readers are peculiarly liable to the fallacy of supposing that they understand the author's reading and purpose because they understand some part or aspect of it... and hence, in judging variants of text, they are led unawares to disparage any word or phrase which owes its selection by the author to those elements of thought present in his mind which they have failed to percieve or to feel."
Again, in §31, he says, "The value of the evidence obtained from Trasnscriptional Probability is incontestible. Without its aid textual criticism could rarely obtain any high degree of security."