Other thing to keep in mind though is that, an ocean is a big places so there are lots of events where life has a chance to start. So even if the individual chance for an event to spawn life is low, you have a lot of chances. Way, way bigger than 1 trillion chances per planet I'd bet.
And after life reaches a certain point, wiping it out is incredibly hard. I don't know what it would take to wipe out all life, as in every last bacteria too, on Earth...
So while I might accede intelligent (especially technological) life might be rare, I sincerely doubt life itself is.
Not meaning to be condescending, that's not how probability works or is expressed.
Also, the fact that the ocean "is a large place" says nothing about how probable or not the events to create and sustain life are.
I understand most people have this gut feeling that because the universe is vast and ancient there must be something out there (and I have it too), but we just don't know.
We just have no idea exactly how hard life is to develop and be sustained. We just started having theories (a handful at that) about how we transcended from chemistry to biology. The prevalent theory for example is that the moon's unusually big size and proximity was the catalyst for that to happen. How many planets have extremely big moons in such close proximity? How many million other factors played a role assuming the tide theory is even close to accurate?
It's just an infinitely complex problem and we just don't know.
Not quite, it's the opposite. We're having a hard enough time theoreticizing how self-replicating nucelotides with adequate lipid-bilayer maintaining molecular machinery occurred naturally on our volcanic, reducing-atmosphere of a planet.
Abiogenesis isn't the same as evolution, and given what limited knowledge we have of prebiotic Earth, life shouldn't have naturally occurred here. Ocean size doesn't matter in this case when the ocean isn't able to form a single self-replicating cell. The dice being rolled don't even have the number you need.
This same argument can be applied to argue that aliens speak English.
The reason we know that aliens don’t speak English is that, as vast as the universe is, the set of possible languages is much larger and so rich with possibility that it need never repeat.
So why do we think the set of languages spoken by chemistry is any different?
And after life reaches a certain point, wiping it out is incredibly hard. I don't know what it would take to wipe out all life, as in every last bacteria too, on Earth...
So while I might accede intelligent (especially technological) life might be rare, I sincerely doubt life itself is.