  We compare two approaches to embedding joint distributions of random
variables recorded under different conditions (such as spins of entangled
particles for different settings) into the framework of classical,
Kolmogorovian probability theory. In the contextualization approach each random
variable is "automatically" labeled by all conditions under which it is
recorded, and the random variables across a set of mutually exclusive
conditions are probabilistically coupled (imposed a joint distribution upon).
Analysis of all possible probabilistic couplings for a given set of random
variables allows one to characterize various relations between their separate
distributions (such as Bell-type inequalities or quantum-mechanical
constraints). In the conditionalization approach one considers the conditions
under which the random variables are recorded as if they were values of another
random variable, so that the observed distributions are interpreted as
conditional ones. This approach is uninformative with respect to relations
between the distributions observed under different conditions, because any set
of such distributions is compatible with any distribution assigned to the
conditions.
