lol what seem to be a very easy explanation, the black tube is a "Fuel Tank Breather hose", has turned into more complex and unsure theories concerning the black tube
I did fuel my bike, it had about 3,1 litres left, and the range should be around 59km, the milage was on that moment 302km or so.
But the bike started to judder....so I decided to tank.
I managed to tank around 20L, on a tank capacity of 17.5 litres

Could be the exces fuel was dripping from that hose? dunno, didnt notice it, I stood on the other side of the bike.
Anyway, after the ride home, spirited riding, I noticed 2 drops on the ground coming from that tube, and even a little bit of smoke coming out of it....
It did smell like gasoline.
This is due to overfilling the gastank, I assume?