@MITer94: OK, again, I’ll admit I don’t understand this stuff well enough to be completely certain how everything fits together. But I’d say these things are not relevant, and just confuse things.
For instance, we don’t know the exact admissions probabilities, so to some degree, they’re all our best guesses. There can always be factors we’re not aware of that make the probabilities higher or lower. That doesn’t mean they’re credences/confidences and not probabilities.
And regarding your dice example, one of the background criteria, A, is also one of the propositions (that you’re trying to determine the probabilities of). In my situation, all the criteria are known beforehand, none of them are propositions. So I don’t think the example is relevant.
All of this gets away from the central point of this thread, that admissions decisions to different colleges are not independent. (Although, re-reading things, I’m not certain you agree with that.)