Privacy issues of recommender systems have become a hot topic for the society as such systems are appearing in every corner of our life. In contrast to the fact that many secure multi-party computation protocols have been proposed to prevent information leakage in the process of recommendation computation, very little has been done to restrict the information leakage from the recommendation results. In this paper, we apply the differential privacy concept to neighborhood-based recommendation methods (NBMs) under a probabilistic framework. We first present a solution, by directly calibrating Laplace noise into the training process, to differential-privately find the maximum a posteriori parameters similarity. Then we connect differential privacy to NBMs by exploiting a recent observation that sampling from the scaled posterior distribution of a Bayesian model results in provably differentially private systems. Our experiments show that both solutions allow promising accuracy with a modest privacy budget, and the second solution yields better accuracy if the sampling asymptotically converges. We also compare our solutions to the recent differentially private matrix factorization (MF) recommender systems, and show that our solutions achieve better accuracy when the privacy budget is reasonably small. This is an interesting result because MF systems often offer better accuracy when differential privacy is not applied.