We just won't know until we've found something. And for us talking now we probably just won't know.
Then you've got to consider that Earth is basically approaching its twilight years. The planet is 4.5 billion years old, macroscopic multicellular life is 600 million to a billion years old. Humans have been around for 100,000 years. In 500 million to a billion years Earth will become uninhabitable again.
Oh and our sun is unusually stable.
Throw all of this together with an added "right type of huge planetary collision" and I feel like you're writing a lot more zeros into that probability.
Of course it's possible that life could take a different path, but there was a lot of opportunity on Earth and it took a long time to get there.
To be fair, carbon is the only base that we have (first-hand) experience with. There _could_ be other bases.
There are very few atoms that allow for the complex scaffolding for shapes. Many atoms are too large (and thus bond too weakly). Silicon is interesting, but it has some difficulties.
https://en.wikipedia.org/wiki/Silicon–oxygen_bond
> Silicon–oxygen single bonds are longer (1.6 vs 1.4 Å) but stronger (452 vs. about 360 kJ mol−1) than carbon–oxygen single bonds.
It is much easier to lock up oxygen and silicon in SiO than in CO compounds and in turn makes them less available for more complex structures of life.