Let's take the sentence
Sentence. Jim was detained on a slim ground that he was seen with Bob two days ago.
The idea is to say that the justification for Jim's detention is weak, and I wanted to express it using the phrase 'on a slim ground'. However, having checked both google ngrams and google search, I found that the phrase 'on a slim ground' and its alternative 'on slim grounds' are not popular at all, so it is probably incorrect to use them.
Question. Is it true that the sentence at hand is not correct, and if so, how to replace 'on a slim ground' to make it correct?