This paper is motivated by major needs for fast and accurate on-line state estimation (SE) in the emerging electric energy systems, due to recent penetration of distributed green energy, distributed intelligence, and plug-in electric vehicles. Different from the traditional deterministic approach, this paper uses a probabilistic graphical model to account for these new uncertainties by efficient distributed state estimation. The proposed graphical model is able to discover and analyze unstructured information and it has been successfully deployed in statistical physics, computer vision, error control coding, and artificial intelligence. Specifically, this paper shows how to model the traditional power system state estimation problem in a probabilistic manner. Mature graphical model inference tools, such as belief propagation and variational belief propagation, are subsequently applied. Simulation results demonstrate better performance of SE over the traditional deterministic approach in terms of accuracy and computational time. Notably, the near-linear computational time of the proposed approach enables the scalability of state estimation which is crucial in the operation of future large-scale smart grid.