A probability distribution describes how likely different outcomes are. It requires multiple observations or an assumed model that can represent variability.

Likely are also making a probabilistic independence assumption.

Probability distributions based on a single data point (of where we know there is life) aren’t reliable distributions.

No, it’s just a starting point. We do need more data.

Which is why they set very wide ranges on the things we know little about. Doing that is less unjustified than guessing specific values, as people have usually done.

It's nowhere near a precise estimate of the probability of life. What it mainly shows is that the Fermi "paradox" is no such thing. It can look that way if we guess specific parameter values, but if we fully account for our uncertainty on the various parameters, then the result is a decent chance that we are alone, given the knowledge we have so far.

I’m not saying precise. I’m saying it isn’t even an estimate.

You can’t have a distribution with one data point.

It’s similar to the arguments about 3I/Atlas being an alien spacecraft because it’s so ‘weird’.

With so few data points, everything is fundamentally ‘weird’ - or normal - we have no way to tell, so making any sort of statistical argument about it is fundamentally useless and misleading, as statistics is based on groups. And we don’t have a group yet.

We know a lot more than the simple fact that civilization exists on our planet. See section 3 for how they estimated the parameters.

One of the most uncertain parameters is the rate of abiogenesis events per planet. For that one they used a log-normal with a standard deviation of 50 orders of magnitude. They discuss specific theoretical limits from biology for both ends of the range.

Compared to this approach, the usual method is to just pick particular values out of a hat. This paper at least improves that by directly representing our vast uncertainty for some of the values.

It doesn't tell us how many alien civilizations there are. But it does tell us the range of possibilities, given what we know and don't know.

Except we don’t actually know the real ranges of values here, so our actual level of uncertainty is still infinite.

If your level of uncertainty is infinite then you're suggesting that abiogenesis could be happening every day in your back yard. I think you might admit we're a little more certain than that.

Really?

Life, once established, is about competition for niche resources. Established life would kick the polypeptides out of a protocell quite easily (with certainty > 99%).

Protocells could be evolving right now at vents in the ocean, with zero of them managing to escape their birthplace due to being outcompeted by things with fully developed organelles.

Fine, let me put it another way. Fill a test tube with simple chemical building blocks of life. Sterilize everything. If our uncertainty is infinite then we aren't willing to say whether metabolizing, reproducing life arises from scratch within five minutes every time we do it.

If you're willing to concede that in fact, that doesn't happen, then you're putting a limit on that parameter, just like the paper did.

In the same sense that we could be certain that life never generated and we’re in a simulation, sure.