How to allocate the probability of success resulting from the joint actions of a group of actors? To address this question, Hou et al. (Operations Research Letters 46, 457-461, 2018) propose to use the Shapley value of a transferable utility game, a “probability game”, assuming probabilistic independence. The purpose of the present note is to analyze the properties of probability games and their duals and to study various solution concepts, in particular the core and the Shapley value. We investigate the axiomatic foundations of the Shapley value on the class of probability games and the link between the different solution concepts, including asymmetric values.