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In previous work, we investigated how space-time curvature influences physical probability distributions. In this paper, we focus on the internal geometry of black holes, studying how an object falling from the event horizon to the singularity undergoes probabilistic deformation due to increasingly intense curvature. By examining the behavior of probability density functions on curved manifolds, we demonstrate that traditional notions of normalization break down near the singularity. This breakdown is rooted in the divergence of geometric scalars and results in a loss of predictive power. Our results suggest that a deeper geometrization of probability is required in regimes of extreme gravitational curvature, with possible implications for black hole thermodynamics, entropy, and information loss. Specifically, we show that as curvature increases, entropy diverges, highlighting a profound connection between curvature and uncertainty in black hole interiors.