Is this supposed to mean more like "What are the odds/probabilites?" This sentence in English doesn't mean much to me
Yes, that's what it means. This sentence is often said when there is a very low probability of something happening.
"Jeg bliver professionel fodboldspiller en dag!"
"(Hvad er) chancen.."
EDIT: It can also be used when something very unlikely happens:
"Jeg har vundet en rejse til Mallorca! Hvad er chancen?!"
Perhaps it just depends on where you are. To me (north GB) this is fine, although the plural is the normal way to say this: "what are the chances". And it's more like an exclamation of disbelief, rather than an actual question.