Probability is the ratio of the favorable cases to all the cases.
Instead of expressing our results in terms of this ratio we make use of another - the ratio of favorable to unfavorable cases. An argument having an even chance can do nothing toward reinforcing others. Taken in this sense it is incontestable that the chance of an event has an intimate connection with the degree of our belief in it. When there is a very great chance, the feeling of belief ought to be very intense. Absolute certainty, or an infinite chance, can never be attained by mortals, and this may be represented appropriately by infinite belief.