  We discuss coupling of violation of Bell's inequality and non-Kolmogorovness
of statistical data in the EPR-Bohm experiment. We emphasize that nonlocalty
and "death of realism" are only sufficient, but not necessary conditions of
non-Kolmogorovness. There can be found other sufficient conditions of
non-Kolmogorovness and, hence, violation of Bell's inequality. We find one
important source of non-Kolmogorovness by analyzing axiomatics of quantum
mechanics. We pay attention to the postulate (due to von Neumann and Dirac) on
simultaneous measurement of quantum observables given by commuting operators.
This postulate is criticized as nonphysical. We propose a new interpretation of
the Born-von Neumann-Dirac rule for calculation of the joint probability
distribution for such observables. It gets a natural physical interpretation by
considering conditional measurement scheme. We use this argument (i.e.,
rejection of the postulate on simultaneous measurement to motivate
non-Kolmogorovness of the probabilistic structure of the EPR-Bohm experiment.
