aspg-40-4291-1792533464 20261020215744 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Pure Mathematics for Theoretical Computer Science PMTCS 2995-3162 2026 6 1 Takaaki Fujita Independent Researcher, Tokyo, Japan Ajoy Kanti Das Associate Professor, Department of Mathematics, Tripura University, Agartala-799022, Tripura, India 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 01 12 4291 https://creativecommons.org/licenses/by/4.0/ 10.54216/PMTCS.060101 https://americaspg.com/journal/40/article/4291 https://americaspg.com/storage/articles/manuscripts/01KYE1Y1B2SMT1JWWHDN3TB69A.pdf