  This paper is devoted to clarification of the notion of entanglement through
decoupling it from the tensor product structure and treating as a constraint
posed by probabilistic dependence of quantum observable A and B. In our
framework, it is meaningless to speak about entanglement without pointing to
the fixed observables A and B, so this is AB-entanglement. Dependence of
quantum observables is formalized as non-coincidence of conditional
probabilities. Starting with this probabilistic definition, we achieve the
Hilbert space characterization of the AB-entangled states as amplitude
non-factorisable states. In the tensor product case, $AB$-entanglement implies
standard entanglement, but not vice verse. AB-entanglement for dichotomous
observables is equivalent to their correlation. We describe the class of
quantum states that are A_u B_u-entangled for a family of unitary operators
(u). Finally, observables entanglement is compared with dependence of random
variables in classical probability theory.
