Automated vehicles are envisioned to navigate safely in complex mixed-traffic scenarios alongside human-driven vehicles. To promise a high degree of safety, accurately predicting the maneuvers of surrounding vehicles and their future positions is a critical task and attracts much attention. However, most existing studies focused on reasoning about positional information based on objective historical trajectories without fully considering the heterogeneity of driving behaviors. Therefore, this study proposes a trajectory prediction framework that combines Mixture Density Networks (MDN) and considers the driving heterogeneity to provide probabilistic and personalized predictions. Specifically, based on a certain length of historical trajectory data, the situation-specific driving preferences of each driver are identified, where key driving behavior feature vectors are extracted to characterize heterogeneity in driving behavior among different drivers. With the inputs of the short-term historical trajectory data and key driving behavior feature vectors, a probabilistic LSTMMD-DBV model combined with LSTM-based encoder-decoder networks and MDN layers is utilized to carry out personalized predictions. Finally, the SHapley Additive exPlanations (SHAP) method is employed to interpret the trained model for predictions. The proposed framework is tested based on a wide-range vehicle trajectory dataset. The results indicate that the proposed model can generate probabilistic future trajectories with remarkably improved predictions compared to existing benchmark models. Moreover, the results confirm that the additional input of driving behavior feature vectors representing the heterogeneity of driving behavior could provide more information and thus contribute to improving the prediction accuracy.