If, in a volume of space, there are N exoplanets and 100 spontaneously created life, then I’d crudely estimate the probability of life at 100/N for a given exoplanet.

Currently, we have only an upper limit on the probability and barely even that. All observations are consistent with a probability less that 10^-40, meaning it certainly wouldn’t happen a second time in the observable universe.

You've not accounted for the tiny number of observations that we've made nor the limited power of our observations. We're not even sure if life existed on the planet literally next to us, let alone these exoplanets. Otherwise I could argue that all observations are consistent with a probability less than 10^-10 or 10^-20 or any other number I feel like.

Ask yourself this, from how many planets in the universe would you be able to observe life on Earth?

How many exoplanets would you say we have proven have no life? You imply 10^40 exoplanets are known to harbor no life. That is probably vastly more than the number of planets in the observable universe (something in the wide region of 10^20 to 10^25).

Something like 5,000 exoplanets have even been discovered. We can’t cross off many of those as certainly lacking life.

I’m certainly not claiming the actual probability is 10^-40 , only using this as an example consistent with an upper limit, which probability would imply life has not arisen a second time in the observable universe. Actually this is way overkill — as you say, even if the probability is as high as 10^-25, life on Earth is still probably the only instance in observable universe. The point is that we have no idea what this all important parameter is.

Our upper limit is something like 10^-1. After all, there is life on earth! Our lower limit is 10^-25 or so.

Why pick the lower limit? Existence of life on earth is extremely powerful evidence.

Ah, but in my opinion we can't call 10^-25 a lower limit since, if life didn't occur in this collection of planets, we wouldn't be here asking the question in the first place!

idk, I think if we see even simple life at multiple points in our own system that we can increase our expectations for the prevalence of life very significantly.

And of course given how vast and indifferent to life the universe is, life would still be vanishingly rare in the universe. It's going to be always precious and a gem.

I agree, if — that’s an enormous “if”.

But it’s actually possible to explore our solar system! We’ve been at it since the 70s!

Yes and I’m glad we’re doing it! No life or fossilized remains of life of any kind has yet been found.

Have we sent up any archeological tools for sample prep and whatnot? Can’t find what we don’t look for, no?

Yup! We've sampled the Moon a number of times, and we're currently trying to figure out how to get one back from Mars...

https://mars.nasa.gov/msr/

Why? That could just mean our solar gave rise to life and not earth alone. Still don’t see why that increases the odds outside of our solar system

If it can spread between planets, it could conceivably spread between stars.

Using this same logic (in an ad absurdum context) we could also say you will never die because no one anywhere has any evidence that you have. That doesn’t falsify your statement, but using ad absurdum shows a statement is not true in every context. I tend to think that shows less conclusion and more investigation may be warranted. That’s how I think of it, but I could be off base and I’m open to being mostly if not entirely wrong.

We have pretty good explanations for why people die and why we expect everyone alive today to die unless we acquire new knowledge that enables us to prevent it.

The God of the gaps.

the epistemology rests on how you construct the question, and the underlying logic.

"Does life exist anywhere besides earth" is a very different question than "does life exist outside these 100 planets". Because they are different questions, the relevancy of data and hypotheses are different.