"it's private I don't have to tell you because it's not your business"
I agree with* @logisticallifeproblem- Odd and unnecessarily hostile response from him. *
Suppose you have to make a call:
When they say not your business...
could it be a topic they think you'd be offended by - for whatever reason... and as such by telling you "the joke" it'd mean a lot more hassle (from you) they would get about it than is worth or exposes them for something they'd rather not be exposed about (think stupid, silly, dark, dirty, blue, tasteless, offensive - whatever etc.)
Or something more sinister... is the colleague more than a colleague?
Personally if i was sending a work colleague a joke on my phone and DH asked what i was up to - id have no qualms explaining what "the joke" was - even if it was a shit joke, nothing to hide, as such i don't get defensive when he asks what i'm laughing at or conversing about because its nothing sinister.