Bayesian orthodoxy posits a tight relationship between conditional probability and updating. Namely, the probability of an event A after learning an event 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. Thus, Bayesian updating seems not to describe the relation between the probability distribution that arises from learning an event B compared to merely supposing it.