Many fallacies and biases in human reasoning and judgment have been reported individually, but their relationships have rarely been argued, and we are still far from a unified psychological theory of thinking. In this paper, equiprobability is proposed as a key concept in human thinking from a Bayesian probabilistic perspective. The importance of the equiprobability assumption, together with the rarity assumption and a tendency to seek information, is suggested from the results of our probabilistic approaches to various tasks. These tasks include deduction, induction, and probability judgment, including the Wason selection task, covariation assessment, hypothesis testing, and base-rate neglect. People seem to have a general tendency to assume the equiprobability of any two target events they encounter. Using ideas obtained from studies of inference in animals and in people with schizophrenia, the adaptive implications of symmetrical inference, based on its relationships with the phylogenetic origins of human creativity, language, and social intelligence, are discussed.