In this paper, a weighted transfer point location problem is developed in which demand points have probabilistic coordinates. The proposed model is formulated as a probabilistic unconstrained nonlinear programming and the optimum values of decision variables are obtained in the form of probability distribution functions. Because of the complexity in solving the developed model by using the traditional solution approaches, a new stochastic inference method called Probabilistic Role Base (PRB) is developed based on the derived optimum probability distribution functions of the decision variables. This method is used to infer the optimum or near optimum values of all decision variables without solving nonlinear programming model, directly. Finally, to demonstrate the efficiency of the developed algorithm, a numerical example is presented and the results are compared with the optimum solution.