"Let's start with what you mean by life." Absolutely correct.
The chance of life in any form increases exponentially as it is more simple. Actually, the other way round is more appropriate: The chance of life becomes less probable as we consider more and more intelligent organisms.
I would suggest that the chances of simple microorganisms are billions to one on. The chances of highly intelligent life, much much less. We should remember, however, that other species on Earth are intelligent - dolphins, for example. It is just that we are the only ones with this level of technology.
I would be very surprised, if there were not at the very very
least one planet per galaxy with organisms of at least our level of intelligence.
One major point to consider is, barring FTL travel, it is extremely impractical for physical transportation between intelligent species, even if they are around stars at the average of 5 light years separation (closer at galaxy centres). However, EM communication is at the speed of light and not that impractical - but still around 8 years between each send and reply. And, as has been pointed out, it is not only necessary for civilisations to be in relatively close proximity in space, but they must also be co-temporal. Try talking to the Ancient Greeks, and their location is only a few thousand miles away.
P.S. When it comes to space, thousands of years means next to nothing.