Frankly, Deuce, it is attitudes like that that hold back scientific progress. If there was something about abiogenesis that made it so it could only happen once, there wouldn't be anything magical about it. What you're doing is ruling out a potential natural hypothesis without any evidence whatsoever, and this, my friend, is magical thinking.
You said it yourself, we don't know that there's other life out there. More to the point, we don't have any evidence to think it is probable or even possible. What information do you have that, in principle, abiogenesis must be able to happen elsewhere? What information do you have that, if it is possible to occur elsewhere, the degree of likelihood is less than the number of stars?
What those "simple laws of probability" you talk about actually tell us is that if we can't fill in the variables then we can't know what the probability is. Do you know what the likelihood of abiogenesis occurring on an Earthlike planet is? If you do, please stop holding out on us and go claim your Nobel prize. If you don't, then it is unscientific to speculate, you're just guessing.