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According to a recent proposal (Shogenji 2012, Atkinson 2012), the degree of justification for accepting a hypothesis should be given in the form of a function of the conditional probability and prior probability of the hypothesis. Shogenji and Atkinson impose a certain condition on measures of justification, and prove that there is only one function (up to monotonic transformations) that satisfies this condition. In this paper we show that Shogenji’s function J is not suitable for the purpose of expressing the degree of justification of hypotheses by evidence. We identify a particular property that the function J shares with most of the known measures of confirmation, and whose possession by a function implies that it will always include a pair of mutually inconsistent hypotheses in the set of justifiably accepted hypotheses given some evidence. We formulate a general criterion that predicts which functions are prone to the problem of mutually exclusive hypotheses, and we discuss what functions can escape this problem.