I think a Poisson distribution is what you're looking for here. Roughly, if events happen independently and with a fixed probability per time interval, you get a Poisson distribution. Poisson distributions apply to a lot of things, so it's a very useful distribution to know about.

But since the number of cars is increasing, it's not a Poisson distribution; if the chance per car per time is constant, you'd expect the time to the next fire to be shorter.