Some simple (but instructive!) calculations can convince us that these two models represent the same situation. The more interesting question is how do these probabilistic models relate to the epistemic-doxastic models of Definition 2.4. Here the situation is more complex. On the one hand, probabilistic models with a graded notion of belief which is much more fine-grained than the “all-out” notion of belief discussed in the context of epistemic-doxastic models. On the other hand, in an epistemic-doxastic model, conditional believes are defined for all events. In the above models, they are only defined for events that are assigned nonzero probabilities. In other words, epistemic-probabilistic models do not describe what a player may believe upon learning something “surprising” (i.e., something currently assigned probability zero).