The quaternion is an effective tool to evaluate uncertainty, and it has been studied widely. However, what is the quaternion probability still an open question. This paper has proposed the quaternion probability, which is the extent of classical probability and plural probability with the aid of quaternion. The quaternion probability can apply classical probability theory to the four-dimensional space. Based on the quaternion probability, the quaternion probability multiplication has been proposed, which is a method of multiplication conforming to the law of quaternion multiplication. Under the bayesian environment, the quaternion full joint probability and the quaternion conditional probability is proposed, which can apply the quaternion probability to address the issues of quantum decision making. Numerical examples are applied to prove the efficiency of the proposed model. The experimental results show that the proposed model can apply the quaternion theory to the bayesian updating effectively and successfully.