According to the philosophical theory of inferentialism and its psychological counterpart, Hypothetical Inferential Theory (HIT), the meaning of an indicative conditional centrally involves the strength of the inferential connection between its antecedent and its consequent. This paper states, for the first time, the implications of HIT for the probabilities of conditionals. We report two experiments comparing these implications with those of the suppositional account of conditionals, according to which the probability of a conditional equals the corresponding conditional probability. A total of 358 participants were presented with everyday conditionals across three different tasks: judging the probability of the conditionals; judging the corresponding conditional probabilities; and judging the strength of the inference from antecedent to consequent. In both experiments, we found inference strength to be a much stronger predictor of the probability of conditionals than conditional probability, thus supporting HIT.