I have a periodic event that has a duration in time $d$. This event always starts happening $p$ days (or whatever unit of time) after the start of the previous event, with $p>d$. Given a length of time $l$ days with $d < l < p$, and given that I don't know when the last time the event happened was (or even if it's happening at the moment), what's the probability that this event will be happening during the next $l$ days? Not necessarily start to finish, just that there'll be some part of this event happening then.
EDIT: By the way, I used "days" as a unit of time here but I want a solution to the continuous problem, i.e. the event can happen at any time during a day, it does not necessarily start at midnight, $d$, $l$, and $p$ are real numbers, etc.