  This work introduces a probabilistic-based model for binary CSP that provides
a fine grained analysis of its internal structure. Assuming that a domain
modification could occur in the CSP, it shows how to express, in a predictive
way, the probability that a domain value becomes inconsistent, then it express
the expectation of the number of arc-inconsistent values in each domain of the
constraint network. Thus, it express the expectation of the number of
arc-inconsistent values for the whole constraint network. Next, it provides
bounds for each of these three probabilistic indicators. Finally, a polytime
algorithm, which propagates the probabilistic information, is presented.
