This paper proposes a unified theoretical model to identify and test a comprehensive set of probabilistic updating biases within a single framework. The model achieves separate identification by focusing on the updating of belief distributions, rather than classic point-belief measurements. Testing the model in a laboratory experiment reveals significant heterogeneity at the individual level: All tested biases are present, and each participant exhibits at least one identifiable bias. Notably, motivated-belief biases (optimism and pessimism) and sequence-related biases (gambler's fallacy and hot hand fallacy) are identified as key drivers of biased inference. Moreover, at the population level, base rate neglect emerges as a persistent influence. This study contributes to the belief-updating literature by providing a methodological toolkit for researchers examining links between different conflicting biases, or exploring connections between updating biases and other behavioral phenomena.