Please do note that if you want to become a professor in a prestigious University like the Delhi University, you need to have a First Class Master's Degree full time from the same or some other UGC recognized University, full time. Regarding you eligibility to do this course, am not too sure. Please check with the University authorities. If you are eligible, plunge into it and take up the Master's Degree. You can then appear for the UGC NET examination in the same subject and qualify. You can also take the Delhi State examination, which is normally called SLET. Once you qualify you are eligible to get a junior level teacher's position. Once you get in, that is the starting point. You must compulsorily do the Part time Doctorate degree.
With the doctorate degree, you also need high quality research publications. To get an idea of the kind of publications needed, please do visit the library of the Delhi University and understand the same. Please do note that these days, the competition is very severe and only those who demonstrate a high level of scholarship, can aspire to become Professors.
In reality, the University of Delhi is the best when it comes to quality teaching. You can also check with the Asoka University, New Delhi, if they have any other creative courses for you to make a career. They do have a Post Graduate Diploma in Liberal Studies, for which a law degree is fine. Kindly check if you will be interested in this course. Of course, you anyway need a doctorate, since your primary interest is in teaching.