  We specify for a general correlation scenario a particular type of a local
quasi hidden variable (LqHV) model [J. Math. Phys. 53 (2012), 022201] -- a
deterministic LqHV model, where all joint probability distributions of a
correlation scenario are simulated via a single measure space with a normalized
bounded real-valued measure not necessarily positive and random variables, each
depending only on a setting of the corresponding measurement at the
corresponding site. We prove that an arbitrary multipartite correlation
scenario admits a deterministic LqHV model if and only if all its joint
probability distributions satisfy the consistency condition constituting the
general nonsignaling condition formulated in [J. Phys. A: Math. Theor. 41
(2008), 445303]. This mathematical result specifies a new probability model
that has the measure-theoretic structure resembling the structure of the
classical probability model but incorporates the latter only as a particular
case. The local version of this quasi classical probability model covers the
probabilistic description of every nonsignaling correlation scenario, in
particular, each correlation scenario on an multipartite quantum state.
