 When sufficiently strong evidence becomes available, it turns out that the contributions of prior plausibility assessments to the values of posterior probabilities may be substantially “washed out”, overridden by the evidence. That is, provided the prior probability of a true hypothesis isn’t assessed to be too close to zero, the influence of the values of the prior probabilities will very probably fade away as evidence accumulates. In Section 4 we’ll see precisely how this kind of Bayesian convergence to the true hypothesis works. Thus, it turns out that prior plausibility assessments play their most important role when the distinguishing evidence represented by the likelihoods remains weak.