Work = force times distance
If a pulley can life 4kg with a 1kg counterweight, then the 1kg mass will move 4 times as far as the 4kg mass will over an interval of time.
any ideal (that is, 100% efficient device) has (work out)/(work in) = 1. (Conservation of energy)
Here it's 4kg * g * 1cm = 1kg * g * 4cm. They're inherently equal in a frictionless device, that's the whole reason mechanical advantage works, it doesn't create energy, just expresses it over more / less distance with more/ less force.
In real life though, there's friction etc, so not all of the energy put into the device "comes out" mechanically, some is lost to heat, sound, so forth. Work is change in energy, so it is clear that efficiency does equal work out / work in. It could not however equal work in/work out, since in real life that number would always be greater than 100%, and a more than 100% efficient device makes no sense.
What you guys were probably thinking of were the relationships
IMA = distance in/distance out
IMA = force out/force in.
However efficiency is also AMA / IMA, which intuitively makes sense given what I wrote above.