Bayes’ Rule dictates how much credence you should put in a given proposition in light of prior conditions/evidence. It answers the question How probable is this proposition?
Popperian falsificationism dictates whether a given proposition, construed as a theory, is epistemically justifiable, if only tentatively. But it doesn’t say anything about how much credence you should put in an unfalsified theory (right?). It answers the question Is this proposition demonstrably false (and if not, lets hold on to it, for now)?
I gather that the tension has something to do with inductive reasoning/generalizing, which Popperians reject as not only false, but imaginary. But I don’t see where inductive reasoning even comes in to Bayes’ Rule. In Arbital’s waterfall example, it just is the case that “the bottom pool has 3 parts of red water to 4 parts of blue water” - which means that there just is a roughly 43% probability that a randomly sampled water molecule from that pool is red. How could a Popperian disagree?
What am I missing?