Living systems have to maintain a particular relationship with the environment by continuing trans-boundary interactions with the environment. To understand how living systems have evolved their ability to manage the uncertainty of the environments, it is needed to formalize the probabilities of events occurring to an internal entity, not to an external, meta-observer, in relation to objective properties of the entity and the environment. I argue that major philosophical interpretations are not sufficient to explain the relationship between objective properties of living systems and probabilities of events occurring to the systems, and propose an alternative interpretation and theory of probabilities of events, named internal probability theory, to apply probability concept to the explanation of the evolution of life. In the internal probability theory, the probability of an event is interpreted as the degree of the uncertainty of events occurring to an internal material entity, not to an external epistemic observer. A mathematical model shows that the probabilities of events that a given subject entity experiences are not simply determined by the degrees of discrimination between different states of the environment by the entity, but determined by the interaction between the subject and the environment, arising from their cognitive properties, such as selectivity and discrimination ability. With the aid of the internal probability concept, the probability of survival can be realized in terms of objective properties of the subject entity and the environment, which may lead us to an understanding of how living systems manage the uncertainty of the environment.