If we imagine that in the last 5 billion years, there have been a good solid 10,000 post-industrial civilizations, and each of those civilizations has lasted 10,000 years (in the post-industrial stage where they're detectable), then that implies that of the last 5,000,000,000 years, 100,000,000 of them have been host to a post-industrial civilization: a given year has on average 0.02 currently present civilizations in it.
Now, this hypothesis does probably imply that significantly interstellar civilizations are impossible, since it seems like if you've colonized say 20 stars, what disaster could possibly end your civilization?
(I think the most likely scenario is that we're the only civilization ever to have developed in the Milky Way. Everything else seems like it assumes a lot of additional stuff.)