  We consider the problem of representation of quantum states and observables
in the framework of classical probability theory (Kolmogorov's
measure-theoretic axiomatics, 1933). Our aim is to show that, in spite of the
common opinion, correlations of observables $A_1, A_2$ and $B_1,B_2$ involved
in the experiments of the Bohm-Bell type can be expressed as correlations of
classical random variables $a_1, a_2$ and $b_1, b_2.$ The crucial point is that
correlations $\langle A_i, B_j \rangle$ should be treated as conditional on the
selection of the pairs $(i, j).$ The setting selection procedure is based on
two random generators $R_A$ and $R_B.$ They are also considered as observables,
supplementary to the "basic observables" $A_1, A_2$ and $B_1, B_2.$ These
observables are absent in the standard description, e.g., in the scheme for
derivation of the CHSH-inequality. We represent them by classical random
variables $r_a$ and $r_b.$ Following the recent works of Dzhafarov and
collaborators, we apply our conditional correlation approach to characterize
(no-)signaling in the classical probabilistic framework. Consideration the
Bohm-Bell experimental scheme in the presence of signaling is important for
applications outside quantum mechanics, e.g., in psychology and social science.
