Its worth checking your miui version on your Note 3 pro, the vendor shipped mine with 7.1.9 which is apparently some custom one which wasn't getting OTAs. Flashed it to the official 7.2.3 which just pulled the 7.2.5 update :3
Who did you order it from? I'm getting mine from TopOne and they had on their page that they will install a custom rom which blocks OTA's and add playstore etc if you don't ask them not to. So i asked them to leave it factory sealed and i'll do it all myself to which they were happy with doing.
It speeds things up as well, as otherwise they take a few extra days sending it out as they have to install software etc. So much better me doing it myself straight from the get go.