The fine-tuning of the Universe

Suppose someone -- let's call him Peter -- were kidnapped, and the kidnapper is a psychopath and sets up some explosion device that is tied to Peter. The device is programmed to shortly generate 10 random numbers. If the numbers so generated are anything apart from 10 zeros, it will instantaneously explode, and hence kill Peter.

So Peter thinks, well this is it then. The chance of me surviving is 1/10^10 or 1 in 10 billion. However, much to his delight, the contraption duly displays the 10 zeros!

So he says to the psychopath "you had me worried there, you must have programmed it to display 10 zeros!".

The psychopath responds, "no no, not at all! It was completely random and you're just incredibly lucky. Don't forget, if it had been any other combination of numbers, you would be dead and wouldn't be here to think about it. You can only live in a world, and hence contemplate your situation, where 10 zeros come up.

Of course, this sounds preposterous and we would surely conclude the psychopath is lying. But does his argument have merit?

This is not just an idle question. It has direct applicability to the fine-tuning of the physical constants of our Universe. Or indeed the fact we were actually born rather than any of the countless potential human beings that could have been born in our place. Or the fact that the human race came into being due to all the improbable events that were required e.g. the meteor impact 66 million years ago etc.