We investigate the discrete (finite) case of the Popper-Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of "knowledge". We develop a probabilistic version of this concept ("degree of safety") and we analyze its role in games. We completely

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... matize the logic of conditional belief, knowledge and safe belief over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing "action models" and a notion of probabilistic update product, that comes together with appropriate reduction laws.