Philosophy to The Rescue

In the case of two competing hypotheses, what determines the final probability of each hypothesis is the product of the ratio between the initial probabilities of the two hypotheses (before evidence) and the ratio of the probabilities that the evidence appears in each case (called the likelihood ratio).

Determining what exactly counts as the "initial probability" of a hypothesis, and the possible ways in which such probabilities can be determined, remains one of the most difficult challenges in Bayesian confirmation theory.