[rgbswan]

> There is some probability that a random star has intelligent life on orbiting planets, but we have no idea what that probability is.

100%. The evolutionary pattern of our solar systems formation and earth ending up, temporarily, in just the right spot isn't rare but (was) a matter of time/timing.

Now one could argue that the stellar objects carrying specific components necessary for life did not hit every or many solar systems but every single simulation (in my head) of the big bang's aftermath reveals that it's at least multiple hundreds of thousands, given how much the observable universe has revealed so far in the places that we looked.