First of all, both likely and probable are inherently vague terms: there is no way of quantifying either, nor are there many options for proving that one is stronger than the other. Some speakers may perceive likely as stronger than probable, others may hold the opposite view, and many will find themselves unable to say.
The vagueness of the terms is underlined by various attempts at "redefining" or "disambiguating" them; cf. Words of estimative probability. These are legit, but have no impact beyond the scope where they have been so defined.
Also, I very much doubt that dictionary entries for likely and probable, even if they do explain either in terms of the other, pay much attention to calibrating the relative strength of these terms, and I would not attempt to take them for their word at this point.
It is just fine to take likely and probable to be of equal strength.
As for register, it is worth considering that likely is of Germanic origin, whereas probable is a French loan; this is still palpable and may tip the scales one way or the other for particular speakers and occasions. That said, stipulating that one is colloquial and the other is formal is just off the mark.
There is a mathematical theory of probability; but it is important to realize that the word probable was borrowed by mathematics from natural language, not vice versa. It goes on living its own life, independent of mathematics. (And a probability theorist cannot take away any of the vagueness of the word probable). Even if what is not called the theory of probability had been called the theory of likelihood instead, it would not have impacted the perception of the two words to any significant degree. (And by the way, both probability and likelihood are strictly technical terms within that theory.)
Finally, either of the two adjectives can function as both attributive and predicative, as can be easily attested by a Google search.
Of course, there are fixed terms, collocations, and idioms (Probable cause; be likely to). Apart from these, likely and probable are interchangeable in collocations such as likely event and probable event.