I will simply say that most people don't really understand the skew. It's telling you about volatility, and while that is related to probability, it's related in the same way the risk free return is: vary the risk free return, and you vary your probabilities. Same with volatility.
But probability is probability, period. I see a lot of fancy terms being thrown around about it, but it's best to keep it simple. In an IC, it's all about the chance of either coming close or actually getting touched on the strike. Because you have to think very hard about what to do once this happens: you're looking at very high gamma, and you don't know what the future holds. Will it continue through, or reverse? You don't know. And you have to know you don't know, and know you won't know when it actually happens.
I only look at the probability of touch, and while I use TOS, which gives you this probability, the probability it gives you is based on a skewed normal distribution, which is not the real world. It's kinda sorta like the real world, but kinda sorta can get you murdered.
So, I worked very hard, before I placed my first IC, on coming up with a realistic probability of touch, not based on anything normal or related to it, and on a strategy to follow once it actually happens. Which it has, this month, so now I'll know whether what I came up with actually works. If not, I'll try something else. I'm only devoting a small amount of money until I really come up with something that does work in this situation, and as I have no deadline other than what I impose on myself, I really don't care if it takes years before I come up with something that satisfies me.
My researches showed me that people have come up with all kinds of different and sometimes truly weird ways of dealing with this. Obviously, the key to IC's is dealing with this correctly, and the only way to truly know which way is correct is to find out through experience. So, that's where I am.