Odds of Getting In
It's tough to say. You might just have to give it a shot rather than asking for odds. The process of getting into the Foreign Service is just a little arduous. And by a little, we mean a lot.
There are multiple portions to the exam and you have to pass each one before moving on to the next. The Foreign Service, in addition to several standardized tests, will want essays, personal statements, background experiences, a security investigation, favorite color, and the names of your relatives and pets. Then there's a medical exam consisting of your entire physical history including height, weight, shoe size, number of dental fillings, toupee size (if applicable), etc.
Then, if you pass the near proctologic-level medical and security checks, you'll face the dreaded oral exam. You'll play the part of an FSO trying to solve some sort of international ordeal while being graded by State Department personnel. Assuming you pass everything else, the oral exam is what determines your final place on what's called the Register, which is the official list the Foreign Service selects its officers from. Best of luck.