ghost of a
Least trace of; slightest resemblance to; smallest bit even of; a very little.
Usually used with "chance" or "idea" in negative sentences, or with "smile".
There wasn't a ghost of a chance that Jack would win.
We didn't have the ghost of an idea where to look for John.
The teacher scolded Harold for drawing a funny picture on the chalkboard, but she had a ghost of a smile.
Compare: FAT CHANCE.