Note how the third valve appears to have two slides coming off of it? That is why the horn looks short.
With no valves depressed, the air probably goes through the slide with the water key, but not the other slide. (The slide with the water key is probably the main tuning slide.) With the third valve depressed, the air probably loops through both slides.
I'm not a Conn person, but it seems like Conn experimented with some strange valve slide configurations like that. It might be a "house brand" Conn of some kind, but I will defer to the Conn experts present.