OK, I just read the link in your post, and I realized that you're referring to something different when you talk about conservation of probability in Bayesian epistemology. I still don't think it has all that much to do with Liouville's theorem, but some of the stuff I wrote above is a little bit irrelevant. Stupid pragmatist! That'll teach me to mouth off without first looking at the links.

Still, my main point stands. The Bayesian version of conservation of probability just follows from the mathematics of probability (plus Bayesian updating). The Liouvillean version follows from the geometric structure of the space over which the probability distributions are defined.