1 in 10 billion trillion is some pretty serious odds.
It does get more complicated if we factor in life happening quickly enough without an extinction event.
But after looking at images like this there is just NO WAY we are the only ones.
What I'm more pessimistic about is how long such intelligence might live. How many civilizations reached a point of harnessing nuclear power and then wiped themselves out with nuclear war?
Think about other earth-centric scenarios, and try and imagine if dolphins or octopuses or fungus or maybe even insect colonies or plant ecosystems had "won" and become the apex lifeforms on earth instead of humans. I wonder just how different concerns like "civilisations" and "war" and "nuclear power" would have played out in those cases? I wonder if assumptions like "industrial revolutions" and the inevitability of scientific discovery being used in detrimental ways like we have done with nuclear science actually correlate with "intelligence"?