Your "ADDED" bit is nonsense.
The odds of intelligent, tool-using life developing could easily be so low that in the entire observable universe (all eighty billion galaxies of it) it only will happen once. This gives us at least ten orders of magnitude difference in possible probabilities, which is not even remotely "precisely balanced".
Earth being "lucky" is meaningless in this context. The whole point of the anthropic principle is that anyone capable of considering the prior improbability of a particular planet giving origin to intelligent life is absolutely certain to trace his origin to a planet that has a posterior probability of 1 of giving origin to intelligent life. If the conditions of the universe are such that only 1 planet in the lifetime of every 1 million galaxies will develop intelligent tool-using life, then we can expect about 80,000 intelligent tool-using species in the observable universe to observe that high infrequency. In none of those 80,000 cases will any member of those species be able to correctly conclude that the prior improbability of intelligence arising on his planet somehow proves that there should be more than 80,000 planets with intelligent species based on the posterior observation that his planet did indeed give origin to intelligent life.
Finally, your second option doesn't actually explain why Earth is not assimilated. If UFAI is highly improbable while natural tool-using intelligence is reasonably frequent, then Earth still should have been assimilated by unfriendly natural intelligence already. A hundred million years is more than enough time for a species to have successfully colonized the whole Milky Way, and the more such species that exist, the higher the probability that one actually would.
Why do we imagine our actions could have consequences for more than a few million years into the future?
Unless what we believe about evolution is wrong, or UFAI is unlikely, or we are very very lucky, we should assume there are already a large number of unfriendly AIs in the universe, and probably in our galaxy; and that they will assimilate us within a few million years.
Therefore, justifications for harming people on Earth today in the name of protecting the entire universe over all time from UFAI in the future, like this one, should not be done. Our default assumption should be that the offspring of Earth will at best have a short happy life.
ADDED: If you observe, as many have, that Earth has not yet been assimilated, you can draw one of these conclusions:
Surely, for a Bayesian, the more reasonable conclusion is number 2! Conclusion 1 has priors we can estimate numerically. Conclusion 2 has priors we know very little about.
To say, "I am so confident in my beliefs about what a superintelligent AI will do, that I consider it more likely that I live on an astronomically lucky planet, than that those beliefs are wrong", is something I might come up with if asked to draw a caricature of irrationality.