The probabilistic satisfiability problem consists, given m logical sentences, with their probabilities to find if they are coherent, and if it is the case, to find new bounds on the probability of an additional sentence to be true. This problem can be extended to handle conditional probabilities. Criticism of the adequacy of this approach to modeling conditional uncertain information, due to Cohen, is answered by showing that additional conditions, e.g. facts, should be introduced in the objective and not the constraints. Ways to express independence are then shown to correspond to two different situations according to presence or absence of a priori impossible worlds. Donkin's rule (similar to Dempster-Shafer correction) and Boole's approach which first computes a priori probabilities, respectively are the required solution methods.