This paper analyses relationships between probabilities of events happening in biological systems (or probabilistic disposition of systems) and cognitive properties of biological entities comprising such systems. Two kinds of cognitive properties are identi"ed as relevant to the current problem: the ability to respond di!erently against di!erent con"gurations of the environment (discriminability of cognition), and the ability to make an appropriate response to maintain a particular relation with the environment (selectivity of cognition). A basic framework bridging the two features of living systems, probabilistic disposition and the cognitive properties, is presented towards a general theory explaining the process generating probabilities of biological events. In this framework, a deterministic model of a system of entities is developed, in which objects are described as subjects that cognize events (i.e. entities as cognizers). Cognition is used in a wider sense, including not only biotic but also abiotic, and cognizers are conceptually distinguished from the meta-observer who describes the system externally. Based on this perspective, this paper seeks to explicate how events can occur in an uncertain, probabilistic manner, if observed from a cognizer viewpoint, even under a deterministic system. Each cognizer is identi"ed with both the set of states that are actually taken, and its motion function which maps its state uniquely to a successor state depending on the current states of itself and of the rest of cognizers constituting the system. The model analysis reveals that the cognitive properties, discriminability and selectivity, of a cognizer can contribute to determining the probability of an event encountered by the cognizer itself*in particular, discrimination reducing the uncertainty in events occurrence for the cognizer. Biological implication of this result is discussed focusing on the concept of the probability of survival and reproduction.