A formula of total probability with interference term and the Hilbert space representation of Kolmogorovian model

In the previous version of this preprint we demonstrated that the Kolmogorov probability model has a very natural representation in a complex Hilbert space. This representation is based on the well known formula of total probability. The Kolmogorov model should be considered as a contextual probabilistic model: elements of a sigmafield represent not events, but contexts (complexes of physical conditions). To map contexts into quantum states, normalized vectors in a complex Hilbert space, we use probability distributions of two incompatible Kolmogorovian random variables, so called reference variables. Thus in our model quantum representation of the Kolmogorov model is just an image of this model through two fundamental reference variables. In quantum physics we use the position and momentum reference variables. In the previous version the Hilbert space representation was constructed only for dichotomous random varibales on the Kolmogorov space. In this version of the paper we do this for arbitrary random variables with a finite number of values. By constructing the Hilbert space representation of the conventional Kolmogorov model we demonstrated that there is no crucial difference between ”classical” and ”quantum” probability as it was supposed by founders of QM. ”Quantum” probability is just a very special representation of ”classical” probability. In particular, in our approach