Decisions under ambiguity depend on both the belief regarding possible scenarios and the attitude towards ambiguity. This paper exclusively focuses on beliefs, measured independent from attitudes. We use laboratory experiments to elicit the subjective belief formation and belief updating process in an ambiguous environment. As a main contribution, we elicit the entire belief distribution of individual subjects. For almost half of the subjects, we can reject the objective equality hypothesis that one's initial prior follows a uniform distribution. The results also show that, when updating beliefs, more than half of the subjects closely follow the Bayes rule. The rest significantly deviate from Bayes. An investigation of a possible bias in beliefs reveals that subjects' beliefs are mostly neutral and do not display pessimism or optimism.