Maybe the correct one is...

1. increase the probability of success
2. have the possibility of
3. preclude the possibility of
4. leave open the possibility of something
5. without the possibility of performing
6. bear the responsibility of
7. be under the responsibility of someone
8. be the responsibility of
9. be the responsibility of someone
10. investigate the possibility that

Found in Turkish English Dictionary
Found in German English Dictionary
Found in French English Dictionary
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