The supervisory control of probabilistic discrete event systems (PDESs) is investigated under the assumptions that the supervisory controller (supervisor) is probabilistic and has a partial observation. The notions of probabilistic controllability and observability are proposed and demonstrated to be necessary and sufficient conditions for the existence of the probabilistic P-supervisors. Moreover, the polynomial verification algorithms for probabilistic controllability and observability are put forward, respectively. In addition, the infimal probabilistic controllable and observable superlanguage for an unachievable specification is calculated as the solution of the optimal control problem of PDESs. Several examples are presented to illustrate the results obtained.