 However, for distributions that are not discrete, so that the set of states is uncountable in an essential way, and events of probability 0 often occur, we can’t use this ratio definition of conditional probability, since it would involve dividing by 0. However, Kolmogorov notes (1933/1950, Ch. 5) that for any suitably nice partition, it is still possible to come up with a definition of conditional probability conditional on events in this partition, satisfying a generalization of the Law of Total Probability, replacing the sum with an integral: