Emotion-Cause Pair Extraction (ECPE) aims to find all potential emotion clauses and their corresponding cause clauses within a document. Existing methods have successfully applied prompt learning to ECPE by constructing independent templates for each subtask: emotion extraction, cause extraction, and pair extraction. However, these prompt-learning-based methods neglect the conditional dependencies in the three subtasks. To address this issue, we propose a novel ECPE method that employs a Bayesian network to model the conditional dependencies between emotions, causes, and their relations. Specifically, we construct different prompts based on diverse emotion categories to obtain more refined emotion information modeling and prediction. Then, through applying an unsupervised clustering method, we generate more comprehensive and accurate verbalizers. Finally, a Bayesian network is utilized to model the conditional dependencies of the three subtasks mentioned above. Experimental results on both Chinese and English datasets demonstrate that our method outperforms existing state-of-the-art ECPE approaches.