Burnt Wiring harness on my 10HP rear engine Snapper

My 20 year old Snapper has a burnt harness. It's down near the oil tube. There are (what looks like) 2 wires going into one side of the harness, and 1 wire on the other plug in the harness. Red wire, black wire and white wire with plug.  They are pretty burnt. With 2 wires in, and 1 wire out, is there a wire missing ?  The mower will not start..Dont know if this has anything to do with that. There is also a large wire that goes to the starter.  See the picture. Someone please explain this to me. I can attach new plug, but how many wires ?