Maslov probability spaces related to the Bose-Einstein and Fermi-Dirac statistics

For systems of indistinguishable particles, we describe probability spaces factored by the equivalence relations identifying configurations which differ by permutation of particles, under the condition that identical states are forbidden (Fermi-Dirac statistics) or admissible (Bose-Einstein statistics). It is assumed that the states of particles have different probabilities; these correspond either to the presence of an external potential, or to a pair interaction potential, or to a collective interaction. The spaces constructed in the paper are related to specific queuing models.