Having no prior experience with scopes, it seems strange to me that when the probe is not measuring anything (~ not connected to a circuit) it measures a small 50Hz (~ my mains are running at 230V 50Hz) signal instead of some random noise. Is this normal behaviour (my scope is a Rigol DS1052E)?
Yes, that's normal. Due to its high impedance the probe acts as an antenna for the 50Hz field from the mains which fills the space surrounding the wiring (i.e. any room in your house). You'll notice that touching the probe will even show a stronger signal, indicating that your body is even a better antenna.
Yes it's normal.
You're seeing a capacitive divider effect. One capacitor is within the scope probe and essentially is connected from the tip to the scope ground. The other much smaller capacitance is across empty space: from the probe tip to any distant 220vac wires in the walls. The empty space around the probe is the dielectric of this capacitor.
Wave your scope probe around and try to find the location of the strongest 50Hz signal. For me it was the metal arm of the spring-arm magnifier lamp on my test bench. (Here in USA it's not 50, it's Nikola Tesla's 60Hz, because everything MUST be evenly divisible by three, as was his hotel room number and the number of laps he'd swim each morning in the public pool!)
Note that the (usually 10Megs) probe impedance is loading down this parasitic capacitive-divider circuit. Try connecting a 1meg reistor between probe tip and ground, and you'll see the 50Hz signal diminish significantly. Ok, now try a 10K resistor. See what's happening? Most circuitry with its well-under-1Meg impedance will short out this 50Hz signal. This signal will rear its head where high-megs impedances are present: e.g. the dangling test leads of your DMM when set to AC volts and sensitive ranges. Or a dangling unused input on a CMOS logic gate will sometimes inject unexpected 50Hz pulses into your system. And the loud 50Hz buzz in an audio amp with faulty microphone grounding is exactly due to this same signal.