"In the case of" or "In case of"

I suggest that, in cases like this, you use a search facility such as

Google ngram: in the case of

That way you will find plenty of examples if the idiom exists.

Click on the links at the bottom of that page to see how the expression is used.

My example

Jane is doing well at school but, in the case of John, I think we need to consider finding a private tutor.

This is equivalent to

Jane is doing well at school but, in John's case, I think we need to consider finding a private tutor.

I am possibly wrong but I would say that 'in case of fire we install fire alarms' but 'in the case of a fire, we use them'. I suggest the lack of an article is an error.