<p>This paper introduces a novel framework for octonion-valued probability theory based on the right-sided three-dimensional octonion Fourier transform (OFT). We define the octonion probability density function and the associated octonion characteristic function, and establish their fundamental properties including uniform continuity, boundedness, and inversion formulas. Using the right-sided OFT, we derive expressions for expected values, moments, and covariances that explicitly account for the non-commutativity and non-associativity of octonion multiplication. Component-wise decompositions of the characteristic function are obtained using parity arguments, and translation covariance properties are established. Several examples illustrate the differences between classical, quaternion, and octonion probability theories. This work lays the foundation for higher-dimensional probability models within Cayley-Dickson algebras and opens new directions for applications in three-dimensional signal processing.</p>