You're making it way more complicated than it is. There's no internal cooldown so the chance is the same for DOT classes and other classes such as mages in arcane spec.
This means if a Spriest can pull 25k without staff, he'll get let's say a 20% boost in DPS on a timeframe of 7 minutes(Which is big enough for the proc chance to show itself regardless of luck). Same happens to Arcane mage, 20% proc rate(Maybe a little less or more becuz of less casts than DOT classes).
So yea it's equal for every caster. BUT! yes there's a but here. The reason they give it to mages or so, could be the fact that they have a burn phase, and many bosses require a burn phase, the boost of DPS on the burn phases is bigger than classes like Spriest which don't have any sort of burn phase like that, so it makes it more of a tactical benefit on arcane mages. That's the reason they give it out to mages first. Or demo warlocks etc.
On the other hand, on a fight that involves LOTS of movement, DOT classes obviously benefit more becuz they'll simply have more procs from DOTS and it boosts it up more.
It's as simple as that, no big calculation needed.