not a ghost of a chance

not a ghost of a chance (that / of) (a very small possibility; if someone does not have a ghost of a chance, they are not at all likely to succeed) — ни малейшего шанса; не иметь даже призрачного шанса на...;

Example 1: There isn't a ghost of a chance that sth will / would happen — Нет ни малейшего шанса / даже призрачного шанса на...

Example 2: Against competition like that, they didn't have the ghost of a chance of winning. (СIDI)

Example 3: There's not a ghost of a chance that he'll be promoted. (Cambridge Dictionary of American Idioms)

See also
[призрачный шанс]
[fat chance]
[stand a poor chance]
[держи карман шире]