Speed and Likelihood

So I'm reading Carl Sagan's posthumous The Varieties of Scientific Experience, and overall it's pretty good. But Sagan does say something about the likelihood of the origin of life that I found nonsensical. He's talking about the origin of life on Earth and how it happened within a span of 500 million years, from the time conditions were probably suitable for the origin of life to the first actual evidence we have for life appearing. And then he says:

It must have happened very quickly. A process that happens quickly is a process that in some sense is likely. The faster it happens, the more likely it is.

Wha-huh?

He then gives lip service to the problem of extrapolating from a single instance of an event, but that's entirely the point. We have very poor understanding of how life originated, so we can't say how likely it was. And the speed with which a process happens does not correlate with the likelihood of that event happening. If somebody does have evidence or an argument to the contrary, I'd like to hear it.

Think of it this way: Let's say you roll 100 dice, and you want to know how likely it is that all of them turn up as sixes. Now, you're not measuring the likelihood of it recurring, just happening once. This could happen on the very first roll, or it could happen after 40 million rolls. Do either of those situations (it happening quickly vs. after a very long time) convey any particular information about the likelihood of the event?