It is in that case probable just in proportion as the said conditions are numerous, and few hindering conditions are in sight. When the conditions are so numerous and confused that we can hardly follow them, we treat a thing as probable in proportion to the frequency with which things of that kind occur. Such frequency being a fraction, the probability is expressed by a fraction. Thus, if one death in 10,000 is by suicide, the antecedent probability of my death being a suicide is 1-10,000 th . If one house in 5000 burns down annually, the probability that my house will burn is 1-5000 th , etc.
Statistics show that in most kinds of thing the frequency is pretty regular.
The company, hedging on the large number of cases it deals with, and working by the long run, need run no risk of loss by the single fires. The probability of his house burning is only 1-5000, but if that lot befall he will lose everything. He has no 'long run' to go by, if his house takes fire, and he can't hedge as the company does, by taxing his more fortunate neighbors. But in this particular kind of risk, the company helps him out. It translates his one chance in 5000 of a big loss, into a certain loss 5000 times smaller, and the bargain is a fair one on both sides.