[lordnacho]

It actually adds excessive structure.

The underlying model is just:

N*f

How many planets are there, and what proportion of them have detectable life?

The f does not have to be structured as fl->fi->fc, although we can see why you'd assume that kind of structure. It's simple to calculate the PI(series) when the model is just a funnel. Like the Million Dollar Money Drop gameshow.

But you could imagine a more complex model of probabilities that branches and merges. There could be events on the bayesian tree that amplify downstream events. For instance, suppose there is some pathway that if reached will leave certain minerals that future civilizations could use. This has happened already on earth at least once: lignin bearing plants could not be easily digested for a long time, and that led to coal formation during the carboniferous period.

You could imagine many such potential trees, but we only have one iteration.