For independent, random occurrences, the probability distribution for delta-T follows an exponential decay. I.e. the most likely time is "right after". Of cours

For independent, random occurrences, the probability distribution for delta-T follows an exponential decay. I.e. the most likely time is "right after". Of course, that "most likely" can still be small. Fun fact: This is true for any chosen point in time, i.e. the prob that this happens exactly one day after your birthday is higher than that it happens two days later.