A common task in many applications is to find persons who are knowledgeable about a given topic (i.e., expert finding). In this paper, we propose and develop a general probabilistic framework for studying expert finding problem and derive two families of generative models (candidate generation models and topic generation models) from the framework. These models subsume most existing language models proposed for expert finding. We further propose several techniques to improve the estimation of the proposed models, including incorporating topic expansion, using a mixture model to model candidate mentions in the supporting documents, and defining an email count-based prior in the topic generation model. Our experiments show that the proposed estimation strategies are all effective to improve retrieval accuracy.