Bayesian orthodoxy posits a tight relationship between conditional probability and updating. Namely, the probability of an event "A" after learning "B" should equal the conditional probability of "A" given "B" prior to learning "B". We examine whether ordinary judgment conforms to the orthodox view. In three experiments we found substantial differences between the conditional probability of an event "A" supposing an event "B" compared to the probability of "A" after having learned "B". Specifically, supposing "B" appears to have less impact on the credibility of "A" than learning that "B" is true. (Contains 1 figure and 5 tables.)