There is a new probabilistic paradigm in the psychology of reasoning that is, in part, based on results showing that people judge the probability of the natural language conditional, if Athen B, P(ifAthenB), to be the conditional probability, P(B∣A). We apply this new approach to the study of a very common inference form in ordinary reasoning: inferring the conditional if not-Athen B from the disjunction A or B. We show how this inference can be strong, with P(if not-Athen B) “close to” P(AorB), when A or B is non-constructively justified. When A or B is constructively justified, the inference can be very weak. We also define suitable measures of “closeness” and “constructivity”, by providing a probabilistic analysis of these notions.