Pure Mathematics for Theoretical Computer Science PMTCS 2995-3162 10.54216/PMTCS https://www.americaspg.com/journals/show/4291 2023 2023 Independent Researcher, Tokyo, Japan Takaaki Takaaki Associate Professor, Department of Mathematics, Tripura University, Agartala-799022, Tripura, India Ajoy Kanti Das Standard probability theory assigns each event a single real value in [0, 1], satisfying non-negativity, normalization, and countable additivity. Hyper-Probability extends this notion by assigning to each event a set of probability values in [0, 1], thereby capturing multiple independent assessments from diverse sources. Super-HyperProbability further generalizes the framework by mapping events to iterated power sets of [0, 1], modeling hierarchical uncertainty across multiple aggregation levels. In this paper, we formally define the Hyper-Probability Measure and Hyper-Probability Distribution, examine their fundamental properties, and demonstrate how these constructs unify and extend classical probability within the Hyper- and Super-HyperProbability paradigms. 2026 2026 01 21 10.54216/PMTCS.060101 https://www.americaspg.com/articleinfo/40/show/4291