One meaning is that summing the probabilities for N=1,2,3, ... and checking how many numbers actually meet the criteria yield the same result in the limit. More

One meaning is that summing the probabilities for N=1,2,3, ... and checking how many numbers actually meet the criteria yield the same result in the limit. More precisely, their ratio goes to 1 as N goes to infinity. Edit: define f(N) as the number of numbers below N that match. Consider the function f(N)/N. We call a function of N the probability of N matching if it asymptomatically approaches f(N)/N.