Bayesianism, that is, the formal capturing of belief in terms of probabilities, has had a major impact in cognitive science. Decades of research have examined lay reasoners' learning and reasoning with probabilities. The bulk of that research has concerned the response to new evidence. That response will depend on the conditional probabilities a reasoner assumes, yet little research has addressed the question of how reasoners respond when they are provided with new conditional probabilities. Furthermore, there are not just open empirical questions as to how lay reasoners actually respond, there are also open questions as to how they should respond. This is illustrated by philosophical debate about the so-called Judy Benjamin Problem. In this paper, we present experiments on belief revision problems in which the new information is a conditional probability. More specifically, we investigate two versions of these problems: one where basic probability theory (as the core of what it means 'to be Bayesian') provides a single correct answer, and one where that answer is under-constrained. The former provide a new type of evidence on the longstanding question of human probabilistic reasoning skill. The latter informs debate on how to expand the Bayesian toolbox to deal with the issues raised by the Judy Benjamin Problem.