Point-of-interest (POI) recommendation has a wide range of application values in smart city services computing. However, extreme sparsity of user-POI matrix seriously affects the recommendation accuracy. Rich contextual information is often utilized to solve data sparsity, whereas how to efficiently integrate them becomes another challenge. To this end, we merge the contextual information into probabilistic diffusion process to propose a novel approach, namely context-enhanced probabilistic diffusion, to generate satisfying POI recommendations under sparse data environment. Firstly, the check-in data is preprocessed to construct the relevant scores that can reflect the relevant degrees between users and POIs expressly. Then, we extract social explicit and implicit trusts from user relationships, and integrate them with time influence to present a time-enhanced social diffusion process to obtain time-social probabilistic score. Next, by merging time factor into geographical distance, a time-enhanced geographical diffusion process is executed to generate time-geographical probabilistic score. Furthermore, we present a context-aware probabilistic matrix factorization to predict the relevant score for a target user on each POI. Finally, unchecked-in POIs with highest predicted relevant scores are recommended for the target user. Experiments executed on real-world datasets suggest that, the proposed approach outperforms the state-of-the-art approaches in terms of the recommendation accuracy.