I got 222 in my NMAT exam, what is my conversion chance for NMIMS Mumbai?

Chances are low at this score. At 222, you can get somewhere around the 96-98 percentile. NMIMS Mumbai is hard to convert at this score. The Mumbai campus accepts admissions at a 235+ score which generally converts to the 99+ percentile. 

But you have a good chance to convert to the NMIMS Bangalore campus. The Bangalore campus accepts admissions at 220+ score, which converts to the percentile at 96-98. Although NMIMS Bangalore is a decent option, I suggest you give it one more attempt (if you have the time). Otherwise, you can join the Bangalore campus, work hard there, and appear in the top 10% of the students.