PS/2 uses 5V signalling over a two wire open collector bus. The clock is generated by the device but can be inhibited by the host. the data line is bidirectional. This is totally different from USB which uses 3.3V quasi-differential signalling.
Some keyboard and mouse chipsets during the transition period (round about the turn of the Millennium) when Microsoft & Intel were pushing the 'Legacy free PC' could do both, and detect what type of port they were connected to (quite easy - if pulled up to 5V talk PS/2 otherwise activate their USB SIE and gate it onto the bus), via a proprietary 'dumb' adapter.
I wouldn't expect most modern keyboards to support both protocols, and old ones from the early days of USB didn't either. I seem to remember a lot of Logitech Keyboards/Mice from that era that supported both, but their adapters were usually not interchangable with other brands. You'd need to check the user manual of the specific model device you have to see if there's any chance that a dumb adapter will work, then will have to get lucky and find an adapter with the correct (almost invariably undocumented) wiring for your device.
Dual interface mode keyboards and mice are nowadays only a historical curiosity. You'd be far better off getting a budget USB keyboard or if you have a really nice legacy IBM or Cherry mechanical PS/2 keyboard, getting a smart USB <=> dual port Keyboard/Mouse adapter.