Installing a Ring Flood Light Camera

I want to install a Ring Floodlight Camera, in place of a motion detector outside the garage. The Motion detector triggers the 4 lights above of the garage to turn on, and there is a switch inside the house that can turn the lights on and off. Additionally, I replaced the lights above the garage with LEDs of the same spec.

I took off the motion detector without taking not of the wiring, but inside the junction box outside of the garage, there is no "hot wire" thats easily identifiable.

Out of the junction box, there is a (1) White wire (2) gray wire (3) bare wire. Out of the ring floodlight camera, there is a (1) white wire (2) black wire (3) bare wire.

Does anyone know what to do in place of no easily identifiable "hot wire", coming out of the junction box?

My initial impressions are:(JB)Bare Wire to(RFL)Bare wire(then ground to junction box);(JB)Gray Wire to(RFL)White Wire;(JB)White Wire to (RFL)Black wire.

My reasoning for the (JB)white wire to (RFL)black wire is that the two neutral colored wires coming from the junction box, seem to be indicative of a switch loop?

Also, I'm wondering if there be a problem with (1) replacing a motion sensor that triggers the lights above the garage, with a ring floodlight and (2) could the LEDs that are currently being triggered by the motion detector, cause problems with the ring floodlight camera?

Thanks in advance.