I suppose it depends on the nature of your crime.
The probation officer assigned to me was emphasising the risk of not returning.
I travelled with a colleague (actually my boss, who had supported my application to probation), as far as I could tell, nothing was different or communicated compared to normal travel. I certainly didn't need to do anything different anyway.
I would say it's likely the case that the probation trust would only know about you travelling abroad if they retrospectively checked your passport movements, i.e., there probably isn't a system in place that traces passport movements of people on probation.