Actually, it is very much connected to the probability of any one randomly selected marriage failing. Any specific marriage, of course, you'll want to look at the rates of similarly-situated marriages (the same sources that give numbers in the neighborhood fo 50% for the overall divorce rate often report different rates for, e.g., first vs. subsequent marriages, and those that I've seen have consistently had lower divorce rates for first marriages and increasing divorce rates for each subsequent marriage.)
It doesn't make sense to exclude some marriages from something and calling it the overall divorce rate, even if there are cases where the most interesting divorce rate isn't the overall rate.
It doesn't make sense to exclude some marriages from something and calling it the overall divorce rate, even if there are cases where the most interesting divorce rate isn't the overall rate.