Definition of Fine-Tuning

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.

The point is that the probability of an observed value can be calculated precisely, but whether this corresponds to fine tuning is a matter of personal opinion.