This paper is devoted to linear space representations of contextual probabilities—in generalized Fock space. This gives the possibility to use the calculus of creation and annihilation operators to express probabilistic dynamics in the Fock space (in particular, the wide class of classical kinetic equations). In this way, we reproduce the Doi–Peliti formalism. The context-dependence of probabilities can be quantified with the aid of the generalized formula of total probability—by the magnitude of the interference term.This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond'.