If it appears to have a small chop to the top, it may be a 37-38 cab. The 37-38 cab was a little shorter the the 36-1/2 (36 2nd Series) cab, not much but some and it is hard to tell them apart unless equiped with the parts that actually identify the year. In either case, that is the correct weather strip, actually called "windlace".
I starts at the bottom of the door jamb, by the floor, on the lock side of the door and is held in place by the pieces that look like miniture bed steel strips, around the top of the door to the top of the windshield post where it switches to the door itself. It goes to the bottom of the door and is held in place by the door window trim, above, and the door panel on the bottom. The windlace must be installed loose enough to allow the door to close. When the door is closed, it fills the space between the cab and the door and does a surprisingly good job of keeping the weather out and the cab fairly quiet.
