Left hose goes into the fresh air intake hose

hello, owner of a 2003 V70 here, who in a rush to jump his car, forgetting that the battery on the back is the one to jump, pulled open the air filter and found this hose hanging out after. When I got in to start it, I recieved a lovely "Engine System Service Required" notification from my car. Does anyone have any idea what this thing is, and if I can get away with not replacing it?

Size comparison to my 8" foot