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With this, paradoxically, only slim hope? (3,6)

Ross

I believe the answer is:

fat chance

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If this is the answer, I'm afraid I cannot explain it.

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(Other definitions for fat chance that I've seen before include "that won't happen" , "Slim hope, paradoxically!" , "It will never happen!" , "No likelihood at all!" , "Slender hope (odd though that sounds)" .)

I've seen this clue in The Sun.
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