Although I am not a native English speaker, I do feel that a 'likely event' is at least slightly more 'likely' than a 'probable event'.
Merriam-Webster's dictionary seems to agree with me.
likely 1) having a high probability of occurring or being true : very probable
But the British references, Oxford, Collins, Cambridge, MacMillan, all say 'likely' is synonymous to 'probable'.
Is it safe to regard 'probable' as synonymous with 'likely'?
Likelihood is a child member of probability.
Probability is the response of the whole spectrum of all occurrences of a phenomenon in a population.
The probability of responses of the population may be an estimate due to a sample taken, or it may be the 100% census of every member of the population.
Let us say that either by sampling or past experience, the probability says that 15% of the population in a city is allergic to peanuts.
What is the likelihood that when I randomly pick a particular person, that that person is allergic to peanuts?
Let's say that after asking an initial 10 persons none of whom are allergic, we can agree that the allergy probability of the population is exerting statistical pressure such that the likelihood for the 11th person being allergic is much much higher than when you asked the 1st person.
However after having asked 20 persons and none of them are allergic, what is the likelihood of the 21st person being allergic, who is a kid who has been munching on a peanut butter sandwich for the past 10 minutes with no effect? Will that 21st person be part of the 15% probability of the city.
Let us say that a village has the low probability of sickle cell anaemia of 1%. After randomly reviewing the first 200 patients, there is a high likelihood within that low probability population that the 201st patient is sickle cell anaemic.
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.
