"Trend in research"? How could that possibly work? Research will tend to clear the low hanging fruit early, which means the easy steps. This tells us nothing about how difficult the difficult steps (if any) might be.

The analogy I like here is those "collect the letters" games you see at fast food outlets and grocery stores. Buy a Happy Meal, get a scratch off ticket. If you collect all the letters in some phrase you win $N million. When you start the game, the trend is great. Letters are arriving and the phrase is filling in. But try as you might, that last letter never shows up. The game ends and you've won nothing. Of course, the way the game was designed was that last letter controls how many winners there could be. All the rest were distractions.

It does however tell us that the "easy" steps are easy, which was never a foregone conclusion. The other steps will remain what they are. It doesn't mean the trend will continue.

I find it weird to use a deliberately rigged game as an example. If one of the previous letters was wrong, the last letter being right means you don't win either. It's like saying the difficult steps are going to be extra difficult because other steps were found easier than expected.

The point is that if you have N independent boolean random variables X1 ... Xn, establishing a lower bound on the probability that some proper subset of the Xi are true doesn't provide any useful lower bound on the probability they all are true.

Sure, my point was only that if the lower bound on the subset is higher than anyone expected, that will increase the probability of them all being true compared to your prior belief. And it will also increase the probability that life is more common.

You could argue that the priors were garbage I suppose. I'm not arguing for any particular probability.

The McDonalds example does not have independent variables as X1..Xn-1 are deliberately increased as Xn is decreased. I'd also argue that origin of life doesn't have independent variables. If chemistry turns out to be more or less powerful in one setting, it should do something for our assessment of other settings, especially when it's similar processes.

The prior belief must have been based on something. Where does a prior belief that ET life must exist with at least a certain probability come from?

The question becomes what do you think the hard step is?

It's not up to me to show that, since I'm not claiming life is rare. It's up to the person making the strong statement that life is (not just could be) common to convince me that there is no sufficiently difficult step. All I need to do is plausibly argue there could be a difficult step. Pointing out the complexity of all known self contained systems capable of Darwinian evolution is sufficient for that.