Definition of Fine-Tuning

I've looked in and out the forum, and found no precise definition of the meaning of fine-tuning in physics.

QUESTION

Is it possible to give a precise definition of fine-tuning?

Of course, I guess most of us understand the empirical meaning of the phrase... but it seem so ethereal, that's the reason behind my question.

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All we can do precisely is give a probability for some physical quantity to have its observed value. For example (subject to various assumptions!) the probability of the cosmological constant having it's observed value is around 1 in $10^{120}$. Since this is absurdly low we say it's fine tuned.
But where you draw the line between fine tuned and not fined tuned is a matter of debate. Most of us wouldn't consider a 10% probability fine tuned, but what about 1% or 0.1%? Particle physics required a $5\sigma$ probability to be considered proof, and this is about 1 in 3.5 million and this is about 0.00003%, so that seems like a reasonable lower bound for not fine tuned. However I'd guess most people would consider considerably higher probabilities than this as evidence of fine tuning.
Isn't it kind of funny to talk about dark energy (via the cosmological constant) when we don't have a physics theory that it fits into? In Einstein's field equations, I'm unsure how we ascribe a maximum value to $\Lambda$ to begin with, but I would assume that eventually we'll come up with a theory that relates it to other parameters, giving a probability distribution function (somewhat similar to some Higgs mechanism parameters). Within that PDF, it could then be more or less likely to be in the hospitable region than what we've assessed so far. –  AlanSE Nov 7 '12 at 16:03
Agreed, and any probability for the observed value of the CC should be taken with a large pinch of salt. It was just the first example I could think of that most people will have heard of. Whether you agree or disagree with any particular probability for the value of $\Lambda$ I think you'd have to concede it appears to be fine tuned. –  John Rennie Nov 7 '12 at 16:13