Okay, I think the "six consecutive Friday the 13ths" portion of this is a red herring, and doesn't change the probability. Unless you are superstitious, or the events in question have notable dependency on human calendars (like, one is more likely to be injured by fireworks on the 4th of July), the date is immaterial. As a way to prove this, remember that the choice of calendar is arbitrary - You could look at those dates through an Aztec calendar, where there is no "Friday the 13th" at all...
Pick any six specific days at random from the same span, and the answer should be the same.