* The program's selectivity: Top-ranked programs receive many more applications than they can accept, leading to very low acceptance rates even after interviews. Less selective programs may have higher acceptance rates.
* The number of interview invites: If the program invited many candidates for interviews, your chances might be lower than if only a few were invited.
* Your performance in the interview: This is arguably the most critical factor. Did you clearly articulate your research interests? Did you demonstrate a strong understanding of the field? Did you connect well with the faculty? Did you ask insightful questions? A strong interview can significantly improve your chances. A weak one can hurt them even if your application was initially strong.
* Funding availability: Even if the faculty like you, the program may not have funding available for all accepted candidates.
* Your fit with the program and faculty: Programs often look for candidates whose research interests align well with the faculty's expertise and available resources.
In short, while an interview is a positive sign, it's far from a guarantee of acceptance. Some programs might have acceptance rates of 10-20% even after interviewing candidates, while others might be significantly higher. There's no way to give a precise percentage without knowing the specifics of the program and your interview performance.