Based on the generalized probability-distribution-interval decomposition, the problem of probability- distribution-dependent stability analysis for a class of systems with stochastic delays is investigated. The information of the probability distribution of stochastic delay is fully employed and a series of sufficient stability criteria are obtained. It is illustrated by rigorous mathematical proof that the conservatism of the proposed stability criteria can be reduced progressively by increasing the number of the probability interval, which establishes a novel hierarchy of LMI conditions. It is rigorously proved that, with the same decomposition of probability interval, the conservatism of the proposed stability criteria is less than the one obtained by time-varying delay decomposition approach in which the probability-distribution of delay is ignored. The computation burden of the proposed method and the time-varying delay decomposition approach is analyzed and compared.