There can be no certainty.
HM Prison Service staff are constantly trying to find places for new prisoners and, with considerable prison overcrowding, that's not always easy. For example, prisoners convicted at Suffolk Crown Court are normally sent to HMP Norwich but some are sent to HMP Chelmsford, while (if no places in the immediate area are availble) others might be sent much further afield (e.g. to HMP Wellingborough, 100 miles away).
However the nearest 'Category B' prison to Fareham is HMP Winchester, so that's probably the most likely. It needs to be remembered though that, while most prisoners are initially sent to a 'local' (Category B) prison, they might not be there for very long as they are then assesssed to find the most suitable prison for them. For a rape conviction that might mean a prison with a specialist sex offenders' unit, which could be well away from the offender's home area.
In the short term though, HMP Winchester is probably the most likely prison to be used but HMP Isle of Wight (made up of Parkhurst and Albany prisons) is another possibility.