This chapter develops a paraconsistent and paracomplete extension of Popper’s theory of relative probability, motivated by foundational difficulties in classical probability theory. Central among these are the treatment of zero-probability conditioning, the conceptual fragility of Kolmogorovian independence, and the inability of classical frameworks to adequately represent inconsistent or incomplete information. Although Popper’s axiomatization provides a conceptually attractive alternative to ratio-based definitions of conditional probability, it remains implicitly committed to classical logic and thus inherits significant philosophical and expressive limitations. By adopting \(LET_F\) , a paraconsistent and paracomplete logical framework, the chapter proposes a theory of probability in which conditional probability is taken as primitive and probabilistic reasoning is no longer constrained by classical assumptions of consistency and completeness. Within this setting, absolute probabilities arise as limiting cases, and classical Kolmogorovian and Popperian probability functions are recovered under suitable logical restrictions. The resulting framework offers a conceptually unified account of probabilistic reasoning under inconsistency and ignorance, resolves the zero-probability problem without appeal to ratio definitions, and clarifies the logical presuppositions underlying probabilistic independence. More broadly, the chapter advances a philosophical reinterpretation of probability as a theory of rational assessment grounded in non-classical logic, extending Popper’s original insights into a more flexible and expressive foundational setting.