Thinking out loud here.....
If you think about household wiring, both the neutral and ground wires share a common buss, allowing the Alternating voltage to flow(make reference) between hot ( black) to either the white or ground wires.
RV 110v electrical systems do not share the reference between 110v ground/neutral and the chassis of the RV.
Only the DC power side is grounded to the chassis.
Wondering if you have some issue with the 110V side making ground to the chassis, and when you touch the stairs, you are proving a path between the frame and the earth
Jim & Kim from Colorado
2014 Eagle 30.5 RLS
2015 Dodge 3500HD SRW 6.7L
Click on my profile for Mods and notes