As web media, such as social networking services (SNS), become more prevalent, the formation of false beliefs through fake news and propaganda has become a significant problem. This study focuses on the cognitive process of users as actively information-seeking agents in web media exploration and proposes WEB-FEP, a computational model of users forming specific beliefs through interactions with web media. WEB-FEP specifically attempts to computationally reproduce confirmation bias in web media exploration by formalizing the trade-off between belief-confirmatory and exploratory actions inspired by active inference. WEB-FEP is validated by comparing the results of simulations with user experiments conducted on a virtual SNS. The results indicate that the initial belief distributions and learning rates modeled in WEB-FEP can successfully reproduce the diverse behaviors of users including confirmatory exploration.