To answer this question, the user needs to have knowledge of the history of world leaders, particularly the first women to hold the position of prime minister in their respective countries.
Option A, Prathiba Patil, is incorrect. She was the first woman President of India, not the first woman prime minister in the world.
Option B, Sirimavo Bandaranaike, is the correct answer. She was the first woman prime minister in the world, serving as the Prime Minister of Sri Lanka three times - first from 1960 to 1965, then again from 1970 to 1977 and finally from 1994 to 2000.
Option C, Hilary Clinton, is incorrect. Although she was a prominent political figure in the United States and served as the Secretary of State, she never held the position of prime minister in her country.
Option D, Benazir Butto, is not the first woman prime minister in the world. She was the first woman to be elected as the Prime Minister of Pakistan in 1988, succeeding her father Zulfikar Ali Bhutto.
Therefore, the correct answer is: B. Sirimavo Bandaranaike.