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In the context of biometrics, matching confidence refers to the confidence that a given matching decision is correct. Since many biometric systems operate in critical decision-making processes, such as in forensics investigations, accurately and reliably stating the matching confidence becomes of high importance. Previous works on biometric confidence estimation can well differentiate between high and low confidence, but lack interpretability. Therefore, they do not provide accurate probabilistic estimates of the correctness of a decision. In this work, we propose a probabilistic interpretable comparison (PIC) score that accurately reflects the probability that the score originates from samples of the same identity. We prove that the proposed approach provides optimal matching confidence. Contrary to other approaches, it can also optimally combine multiple samples in a joint PIC score which further increases the recognition and confidence estimation performance. In the experiments, the proposed PIC approach is compared against all biometric confidence estimation methods available on four publicly available databases and five state-of-the-art face recognition systems. The results demonstrate that PIC has a significantly more accurate probabilistic interpretation than similar approaches and is highly effective for multi-biometric recognition. The code is publicly-available.