Let's just say that, statistically speaking, the odds of landing a job with MBB are typically less than 1% at the application stage.
However, that's also because MBB attract a lot of really bad applications that have no chance of ever progressing. And if they do, a lot of candidates are completely unprepared for MBB interviews when they show up for them.
If you have a reasonably good background and a good application, your chances of getting a foot in the door change dramatically. And once you're at the interview stage, it mostly comes down to your abilities and dedication. There's also luck involved but you can minimize that.
My point is that statistics shouldn't matter much to you :)
Let me know if there's anything I can do to help!