Rolling bearings are subject to various faults due to its long-time operation under harsh environment, which will lead to unexpected breakdown of machinery system and cause severe accidents. Deep learning methods recently have gained growing interests and extensively applied in the data-driven bearing fault diagnosis. However, current deep learning methods perform the bearing fault diagnosis in the form of deterministic classification, which overlook the uncertainties that inevitably exist in actual practice. To tackle this issue, in this research we develop a probabilistic fault diagnosis framework that can account for the uncertainty effect in prediction, which bears practical significance. This framework fully leverages the probabilistic feature of Gaussian process classifier (GPC). To facilitate the establishment of high-fidelity GPC, the tailored feature extraction with dimensionality reduction method can be optimally determined through the cross validation-based grid search upon a prespecified method pool consisting of various kernel principal component analysis (KPCA) methods and stacked autoencoder. This strategy can ensure the complex nonlinear relations between the features and faults to be adequately characterized. Furthermore, the sensor fusion concept is adopted to enhance the diagnosis performance. As compared with the traditional deep learning methods, this proposed framework usually requires less labeled data and less effort for parameter tuning. Systematic case studies using the publicly accessible experimental rolling bearing dataset are carried out to validate this new framework. Various influencing factors on fault diagnosis performance also are thoroughly investigated.