Recovery broken -> “adb devices” doesn't find my Xiaomi Mi3
I might have misinterpreted your question, but to enable ADB to list Xiaomi devices, you need to update adb_usb.ini and put Xiaomi vendor IDs there:


On windows go to c:/Users/{your-username}/.android
On Linux ~/.android
Open the file adb_usb.ini in a text editor and add these three lines:

0x8087
0x2080
0x2717
Save the file, open a CMD (or terminal) and enter the commands:

adb kill-server 
adb start-server 
Reconnect the device, type this in CMD, now it should be recognized.

adb devices



Source here.