Common probability models include single-event probabilities and probability as the ratio of the number of occurrences of a particular outcome over the large and possibly infinite number of possible outcomes (the frequency model). The odds a to b is a third probability model, equivalent to the probabilities a/(a + b) and b/(a + b)
Science has a strong bias towards the measurable. Mathematics has beautiful and interesting theorems with hypotheses that are incompatible with potential applications. There is a tendency to push for practical results using constructivist or computational methods. New applications of probability should be carefully considered to insure appropriate use.
The frequency model runs into mathematical difficulty in both definition and execution; in particular, it is difficult to deal with large or infinite possibilities, and difficult to characterize the resulting probability values. Thus the frequency model is rejected as a hypothesis, and will be derived as a thesis from other models.