Predictability is a key property allowing one to expect in advance the occurrence of a fault in a system based on its observed events. Existing works give a binary answer to the question of knowing whether a system is predictable or not. In this paper, we consider discrete event systems where probabilities of the transitions are available. We show how to take advantage of this information to perform a Markov chain based analysis and extract a variety of probability values that give a finer appreciation of the degree of predictability. This analysis is particularly important in case of non predictable systems. We consider a "light" analysis that focuses only on predictability as well as a "deep" analysis that handles in a uniform framework both predictability and diagnosability.