Current/milliamp rating of adapter versus device requirement
First, Current draw: Your laptop adapter output is rated for 1580 mA output draw.
Since your mic adapter ouputs less than that (and the microphone must require less than that), the current draw aspect is fine.

Next, Voltage: Voltage at your mic adapter output was 20V, so presumably the mic requires around 20V. The voltage at your laptop adapter output is 19V. This MIGHT be an issue - Check the operating voltage specification of your mic itself (not the adapter). If you have access to the mic's datasheet, check to see if it can function at a supply of 1V less than the the 20V.

Actually, even if you don't have the datasheet, you could just practically connect and test it out. You won't have any problems because you're on the safe side for both the voltage and the current requirements.