  We investigate a state discrimination problem in operationally the most
general framework to use a probability, including both classical, quantum
theories, and more. In this wide framework, introducing closely related family
of ensembles (which we call a {\it Helstrom family of ensembles}) with the
problem, we provide a geometrical method to find an optimal measurement for
state discrimination by means of Bayesian strategy. We illustrate our method in
2-level quantum systems and in a probabilistic model with square-state space to
reproduce e.g., the optimal success probabilities for binary state
discrimination and $N$ numbers of symmetric quantum states. The existences of
families of ensembles in binary cases are shown both in classical and quantum
theories in any generic cases.
