The chance of skill up on a success is dependent on your skill and the formula, I am not sure if is posted somewhere here or came from Ngreth back when the TS cap was increased to 300. I know that at 299-300, it is 5% on success.
As far as the chance of skill up on failure, this is determined by your primary stat. If your primary stat is 0, then you have 0 chance of skill up on a failure. There used to be a list of the required primary stat values needed to max the chance of skill up on a failure. The highest ones (I think brewing and one other skill) required a primary stat of 800 to max the chance of skill up on a failure, equalling the chance of skill up on a success.
I would suspect that the overall chance of skill up takes your chance of succeeding on the combine times the chance of skill up on success + the chance of failing the combine times the chance of skill up on a failure. I do not know if the code for the calculators on the site are still available to the admins or creators of them. However, there is an advanced calculator that has options to account for costs and projected costs if you go to the advanced one.
Hope that helps.