Concerning an old (but still quite alive) rebuttal of the theorem of John Bell

In a old paper by G. Lochak, it is claimed that the Bell definition of a hidden variable is in conflict with the formalism of quantum mechanics. This result implies that it is not necessary to invoke non locality to explain the violation of the Bell inequality. A careful analysis of the concept of probability for hidden variables, as defined differently by Bell and Lochak, show that the reasoning and main conclusions of are not correct.