The paper investigates the direction-of-arrival (DOA) estimation of narrow band signals with conventional co-prime arrays by using probabilistic Bayesian neural networks (PBNN). A super resolution DOA estimation method based on Bayesian neural networks and a spatially overcomplete array output formulation overcomes the pre-assumption dependencies of the model-driven DOA estimation methods. The proposed DOA estimation method utilizes a PBNN model to capture both data and model uncertainty. The developed PBNN model is trained to do the mapping from the pseudo-spectrum to the super resolution spectrum. This learning-based method enhances the generalization of untrained scenarios, and it provides robustness to non-ideal conditions, e.g., small angle separation, data scarcity, and imperfect arrays, etc. Simulation results demonstrate the loss curves of the PBNN model and deterministic model. Simulations are carried out to validate the performance of PBNN model compared to a deterministic model of conventional neural networks (CNN).