Chris, is that blue and black thick hose the hose that's dripping or flowing water ?
If so, i have never seen anything like that and can only assume that it's something that was fabricated to drain water faster, plumbed into the low point drains or freshwater tank drain.
Its large to improve the flow for faster emptying . If that's the case, then I would look for a petcock attached to it, maybe inside the trailer somewhere . I would think it's open or partially open. I would start looking inside the trailer directly above that tube.
Pour water down the sink drains and see if that blue/black hose is attached to the drain system. Maybe someone did a by-pass of the grey water tank for whatever reason.