A math whiz could sum this up quite succinctly: the ratio of probabilities of a forward and reverse path is the exponential of the total entropy increase along the forward path. This exponential growth is exactly what happens to your bank account when interest is compounded. For a bank that gives ten percent interest, your bank account would almost triple in ten years. It grows to more than seven times after twenty years and explodes to twenty times the initial investment by thirty years.
This is why people should start saving for retirement earlier rather than later, and it's also how the relative likelihood of the forward path grows with the entropy increase.