In this talk, we extend or generalize the classical free probability over the complex filed to free probability theory on arbitrary ring with the help of bimodular structures over any fixed ring. In particular, we are interested in the case where a given ring is commutative and unital. Interestingly, if a ring is both commutative and unital, then the Moebius inversion holds as in the classical free probability theory. As applications, we consider free probability theory over scaled-hyperbolic numbers covering both classical free probability theory and those over the dual numbers and hyperbolic numbers. Some interesting free random variables are defined, and their free-distributional data are characterized.