likely、possible、 probably、feasible
The best way to answer your question is to think of a situation where you can use these words. The difference is not based on formal or informal. The difference is based on degree. What do I mean?
Let's pretend as if I asked you will you cook dinner tonight. (So to use these words, you generally refer to some future event.)
if 0% = no, and 100% = yes, then these words fall in between those two percentages.
Possible means some event is going to happen as long as nothing prevents it from happening.
Example:
Will you cook dinner tonight?
Reply: Possible, unless my boss makes me work overtime again.
Feasible means you have a desire to do something and you can easily do it.
Will you cook dinner tonight?
Reply: It's feasible, but I've cooked dinner every night this week, you should dinner once in a while.
Likely means you have a strong degree of certainty
Will you cook dinner tonight.
Reply: I love cooking dinner for you, babe, so most likely I will do it tonight as well.
Probably means that you even even more certainty than just likely.
Will you cook dinner tonight?
Reply: Probably, have you ever seen me not cook dinner?
None of these words imply 100% certainty. So if you actually didn't cook dinner, you can say, I never said I would cook dinner. I said, ("I probable/likely, possibly will cook dinner because at the time that I made that statement, I thought it was feasible.")