As you describe the problem - being able to stop the flow of gas thru the hose by shutting off the petcock - describes a classic case of the float value in your carb being stuck open, most likely by dirt. But your description of where the hose goes doesn't sound like the carb overflow tube - I'd check where the hose goes and if it ends at the carb your float is stuck open - easy to fix yourself if you have modest mechanical skills or a fast, easy fit at an independent shop. As someone else suggested also check the filter screen in the tank as the dirt had to get past that to get to the the carb.

 

My buddy has the same problem with his 94 883. He does need to rebuild and maybe change the screen in tank, havent thought of that, thanks!!!!. But what works for him to fix the problem temporarily is to shut off the fuel, run that sucker real hard till it dies out at speed, turn gas on and restart. Then his float unsticks and no more gas leak. I am going to tell him about all the other suggestion.

His bike has only 5,000 miles on it and it is a 94, ya think it sat around much?? Hahaha. And it was owned by some hillbilly, i am kinda a hillbilly but this guy was a full fledge, back woods, cousin humpin, animal humpin, non mechanical type hillbilly. No offense to any hillbillys out there, as i am one too!!! Want yer coke in a poke???

We were at a stop light after a local bike night, he dropped about a half gallon or so of gas at the light across from filling station. Then about dropped the bike trying to pick up speed in a gas puddle. Thru gas and road grime on my buddies 08 fxdc.