Motivated by the need to identify erroneous disparity assignments, various approaches for uncertainty and confidence estimation of dense stereo matching have been presented in recent years. As in many other fields, especially deep learning based methods have shown convincing results. However, most of these methods only model the uncertainty contained in the data, while ignoring the uncertainty of the employed dense stereo matching procedure. Additionally modelling the latter, however, is particularly beneficial if the domain of the training data varies from that of the data to be processed. For this purpose, in the present work the idea of probabilistic deep learning is applied to the task of dense stereo matching for the first time. Based on the well-known and commonly employed GC-Net architecture, a novel probabilistic neural network is presented, for the task of joint depth and uncertainty estimation from epipolar rectified stereo image pairs. Instead of learning the network parameters directly, the proposed probabilistic neural network learns a probability distribution from which parameters are sampled for every prediction. The variations between multiple such predictions on the same image pair allow to approximate the model uncertainty. The quality of the estimated depth and uncertainty information is assessed in an extensive evaluation on three different datasets.