FZS600 / loose hose from carburation

[Ulympos]

Yesterday I thoroughly cleaned the bike after a very wet weekend with my buddies. When I finished removing dirt from behind the cylinders, I saw this loose hose on the left side of the engine block. In the photo, it is between the clutch cable and the long hose going down (I guess it is the fuel tank overflow). Can someone tell me where I need to connect this shorter loose hose? It comes from somewhere between carburetors 3 and 4.

I do know that there is an opening on the back (not visible) of the front sprocket cover where the loose hose could fit in. A carburetor overflow perhaps?
Maybe someone could take a close-up photo showing how this hose should be installed. Thanks in advance.

UPDATE:
For the moment I led the hose opening into the gap on the backside of the sprocket cover. The second picture shows on the right the clutch cable. The position of the rubber hose in the gap is just under the hex bolt.

[b1k3rdude]

Check where the other end of the hose is connected first, of the top of my head that looks like an overflow hose for when you drain the carbs.

[Ulympos]

Check where the other end of the hose is connected first, of the top of my head that looks like an overflow hose for when you drain the carbs.

"It comes from somewhere between carburetors 3 and 4."... Counting from left to the right. And yes, I expect it is some kind of overflow and on the loose end of the hose no hose clamp.

But if someone will post a clear close-up picture about that area above the clutch/sprocket cover as I did, that would probably clarify a lot.