It is shown that the anytime deduction procedure for probabilistic entailment of Frisch and Haddawy does not have the correctness property when the probabilistic knowledge base considered is not consistent. Moreover, it provides no systematic way of checking consistency. A two phase procedure, using first linear programming and column generation to check consistency, and then anytime deduction, is proposed in order to keep a main advantage of this last method: provide an explicit justification of the bounds entailed by the knowledge base.