If by top 3 you mean Harvard, Stanford & Wharton, then no, not a chance. In fact, I can tell you that your JD will definitely hurt you when applying for Harvard or Stanford. At Wharton, it's a non-factor at best. For example, Stanford only admitted 1 JD & 1 MD last year (might have been stats for the year before). I would bet big money that the JD was from Harvard, Stanford or Yale. When you say you are getting a JD from a top 15, I will assume that means not top 10 or top 5. Top business schools would view it as diluting their brand.
As others pointed out, you will need to decisively show why you need an MBA after doing nothing with your JD. You will also need to demonstrate past leadership & teamwork - preferably in a business setting. Interviewing will only be a factor if you can overcome these other challenges to actually earn an interview.
For most of the top 15 or so schools, the three years you have spent obtaining a top 15 JD will, at best, be considered a non-factor. Three years of work experience would be infinitely more valuable for a business school application. Business school admissions is different that law school. The other stuff actually matters for business school.
For the record, I have a JD from Michigan and 2 years of work experience with AMLAW 15 firms in LA & NY. I also launched my own business 4 years ago and I have a 780 on the GMAT. I consider myself not competitive at Harvard, a long shot at Stanford; we'll see about Wharton.