As organizations increasingly rely on data-driven methods to support decision-making, ensuring fairness in their processes becomes critical. Fairness in responsible process mining involves preventing unfair outcomes and recognizing potential biases that may arise in the different stages of process mining initiative. Acting fairly entails treating individuals equitably, irrespective of inherent or acquired characteristics such as gender, race, or disability, while ensuring compliance with legal and organizational fairness standards. While fairness in process mining has been explored in prior research, there remains a lack of conceptualization to identify, understand, and address fairness issues. To bridge this gap, we propose FairPM, a taxonomy that conceptualizes biases in process mining and the corresponding interventions to mitigate them. Our approach builds on theory adaptation as research method. It integrates an adaptation of biases and interventions from prior machine learning research into process mining. We illustrate the applicability of FairPM through three scenarios, demonstrating its relevance for both academia and industry. This research contributes to the growing field of fair process mining by providing a structured conceptualization that enables researchers and practitioners to diagnose biases and implement fairness interventions, ensuring equitable and unbiased process mining outcomes.