It is just a natural case of the exponential distribution, which is widely used to model expected waiting time. I wouldn't call it 'rare'. Absent other observa

It is just a natural case of the exponential distribution, which is widely used to model expected waiting time. I wouldn't call it 'rare'. Absent other observations and/or priors, the best estimate of your expected waiting time is the amount of time you have already waited. So if you've been waiting 10 minutes for something to arrive, your best estimate of how much longer you have to wait is 10 minutes. If you've been waiting 10 years for a tech to become outdated, your best estimate for how much longer it will take is 10 years. People usually use buses as an example. So it makes sense: if the bus is supposed to come every few minutes, and it hasn't come in the last 15 minutes, then odds are something is wrong thus increasing the prob that the additional wait will also be 15 minutes.