To answer the question about if life is rare we need to visit Europa and Enceladus in our solar system. If those places have life, then life might be quite common in our universe. If they do not have life, then we are likely very alone in the universe.
Maybe the probability that that life will occur is one planet out of every thousand planets. Then the probability of Europa having life is small. However one out of a thousand in a universe with billions of planets is a meaningful number. If this is the case, then examining our own solar system for life, which is comprised of far fewer then 1000 planets, will not be a worthwhile endeavor.
I think the key is understanding the process itself. What does it take to create the minimal self replicating machines necessary to evolve into the complex forms we see today? Once we are aware of the processes involved in the formation of life then we have the context to hypothesize about the probability that these reactions will spontaneously occur.
Things like the Drake equation are meaningless and made up. You can easily make up an identical bullshit equation about the chances of a 747 spontaneously being thrown together on another planet. We can easily see that it's impossible because we know how the 747 is made, we have context. For life? We have no context, no knowledge of where it came from, and therefore the drake equation and any other statement about life on other planets is meaningless.
We have plenty of context for how life forms - organic chemistry! Lets not pretend life is some magical thing - its an organization of carbon, hydrogen, oxygen and nitrogen. And those things just adore linking up in enormous variety given the right temperature and water.
Early Earth was an unimaginably huge petri dish where every grain of sand on every beach was an organic experiment, with the sun, tides and seasons trying every combination of heat/cold/wet/dry/acid/base... in endless cycles. Those conditions are far from unique in the universe. You could argue its inevitable that life/chemistry will unfold in the same patterns on millions of worlds.
Organic chemistry is a incomplete description. The entire field of biochemistry is an incomplete description. Until we can create life from nothing in a petri dish we don't know whether it is an inevitable outcome or a lucky one.
You can argue that the entire earth is a petri dish for a boeing 747. We have all the necessary materials, all we need is a hurricane to throw all the materials together in the right configuration and boom! 747. With billions of planets in the universe it's bound to happen on another one! It's inevitable.
Perhaps this would be more clear: We don't have Enough context to talk about the probability of life on other planets. Perhaps the chemical reaction needed to create life was mind boggling complex, billions of steps needed to happen in the exact order, under conditions that are equally exacting . Or maybe it's devastatingly simple. We just don't know...
Lets take a look at the jet example from another perspective.
The jet is self assembled by proxy of humans being self-assembled. A 747 is the result of a trillion step chemical reaction that stretches across the history of life on earth itself. The chances of this reaction self-assembling on another planet under the same conditions and in the same manner are impossibly low.
What we don't know is whether or not the chemical reactions forming the first life form on earth happened in the same improbable way. Did it happen over eons? did it require a billion steps? I dunno. Nobody knows. It is not unrealistic to say that the chemical reactions necessary to form life are so rare that earth is the only planet in the universe with life.
