The most common and most likely answer to this crossword clue is the 3 plus 6 letter word FAT CHANCE
I've seen this crossword clue in The Daily Telegraph
F
A
T
C
H
A
N
C
E
More clues leading to the result FAT CHANCE
- Precious little possibility of putting on weight
- Large risk? Not likely!
- No way for solid opportunity
- Likelihood of the morbidly obese avoiding health issues?
- Possibility of getting drunk – fetch a can!
- Far from slender odds? Definitely not!
- Big break that won’t happen
- Conversely it means there is only a slim hope
- Remote possibility to get drunk — fetch a can!
- Yet it’s likely to be a slender hope
Buddy explains!

The straight part
We know that "Conversely it means there is only a slim hope" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case conversely it means there is only a slim hope = fat chance.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.