With less air pressure, the same amount of vacuum would create less suction force.
I mean, if I’m in air at 1013 millibars pressure (mean sea level), and I turn on a vacuum pump whose internal pressure is 600 millibars, that’s 413 millibars of suction (i.e. 413 millibars of overpressure forcing its way into the pump). BUT, if I’m in air at only 700 millibars pressure, and my vacuum pump creates the same 600 millibars of internal pressure, that’s only 100 millibars of suction – less than 1/4 of the suction I was generating at sea level!
I went to grad school in Utah, which is also 'way up there. The first time I used a vacuum system, I was seriously bothered that I couldn’t get my system all the way down to low pressure. It kept hanging on, well, above what it should have been to let me turn on the diffusion pump. No amount of leak-checking served to find the source of my leak. Then I realized that I was in the Land Where You Use the Directions on the Side of the Cake Mix, and that my rough vacuum gauge had been calibrated by the Flatlanders down at sea level.
So my vacuum pump had to suck less in Salt Lake City.