Trevor
A couple of issues with your post. Points of order, perhaps.
". . . about the comets that seeded life here . . ."
That may have seeded life here. As you say, life is just "a bunch of chemical interactions" and those chemicals are "bloody everywhere". 'Spontaneous' creation of various precursor compounds has been observed and one of the big barriers - the bonding of ribose and nucleotides - has been rendered that bit less problematic with a plausible alternate process whereby ribonucleotides can be generated without requiring 'free' ribose.
'The probability of life arising on another world is down to one simple question: "how rare are Earth-like planets?"'
Not so. It's down to several questions but one of the biggest ones is: "does life need an 'Earth-like' planet?". The answer is: "Probably not", meaning that life is even more probable. Still, I feel that the Earth is rather special (though highly unlikely to be unique) because it is a combination of a lot of factors. I just don't believe that 'life' really requires all those factors. Life as we know it does, but it is spectacularly closed-minded to believe that any possible life must be as we know it. (I am not saying that you are suggesting anything of the sort, of course.)
"But I would bet my life, and lives of everyone on this mudball that we are not alone."
Hmmm . . . Well, that depends on what you classify as 'alone'. Other sentient life or any type? If we talk about any complex life then less likely to be so confident. Why? Because 'humans' have only existed for (at a high estimate) 200,000 years. Given the most generous estimates of planet formation of ~2bn years after the big bang, humans have been around for about 0.0017% of that ~12bn years in which life has been possible.
The question is not whether life HAS or WILL arise on other planets - that, statistically is almost certain. The real question is whether we are, currently, the only sentient life in this universe. For me, I count that as 'alone'. A semantic differentiation perhaps but I do not class something akin to cyanobacteria as 'company'.
The REAL question, I suppose, is: "is humanity the current pinnacle of 'life' in this universe?"
Even putting that aside, we are alone. Utterly, inescapably so. While the sheer size of the universe makes in vanishingly unlikely that we are the only 'life' to ever come into existence, it also makes if unlikely that we will ever meet another sentience.
How would we?
Chance alone. Pure, desperate chance. Even at light speed, it takes a long time for our signals to reach anywhere. They would have to reach a civilisation at a time when they were capable of receiving it and they would have to have or develop the capability to reach us (somehow) before we were no longer on the planet our signals originated from. Or vice-versa, which is equally unlikely.
The unfortunate reality is that any "intelligent" signal we may recieve is quite possibly from an extinct civilisation.
Plotting the expected trajectory of the universe, in ~150bn years (quick google search), our own, merged, supercluster will be the only thing in the observable universe. It will be impossible to travel or communicate outside of this bubble.
That will of course bring multiple galaxies together, but space is bloody roomy and even with the collision of the combined 1.3 trillion stars of Andromeda and our own Milky Way, there is next to no chance that any stars will actually collide. (Quick wikipedia search : )
Ramble, ramble, but my point is that while the universe has a LOT of stuff in it, it is spread out over truly mind-buggering distances.
So, as likely as life is, isolation is just as assured.
Someone didn't take their meds today.