In the UK, AC mains has a frequency of 50hz so I would guess that your probe has a problem with its shielding and is simply picking up EMI from the mains. If the shielding is not earthed properly all the way down to the tip, the wire will act a bit like an antenna and pick up all manner of stray EMI. Do you get continuity from the metal plug up to the outer shielding at the tip of the probe?
From reading some of the threads on Rigol scopes (I'm thinking of getting a DS1054Z myself) I understand that occasionally probes supplied with Rigol scopes have been found to be faulty. However, Rigol, will usually replace them.