The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal with some decisions problems under uncertainty. This extension relies on a differentiation between the agent-controllable decision variables and the uncontrollable parameters whose values depend on the occurrence of uncertain events. The uncertainty on the values of the parameters is assumed to be given under the form of a probability distribution. Two algorithms are given, for computing respectively decisions solving the problem with a maximal probability, and conditional decisions mapping the largest possible amount of possible cases to actual decisions.