Bayesian Blues: Possibilities with Probability 0

If my read of the landscape is correct (and it may not be), Bayesian views (relatively broadly construed) enjoy a certain dominance in formal epistemology. No doubt this is because the various explorations into Bayesian formalisms have provided philosophers with rich theoretical resources and aided in the development of many significant advances in formal epistemology. However, despite whatever virtues they have, these approaches wind up saddled with some results that are, prima facie, highly counter-intuitive. The specific counter-intuitive result that I've been thinking about recently has to do with possibilities that get assigned a probability of 0.