How was Yusuf (Joseph), peace be upon him, imprisoned despite the clear evidence of his innocence from the tearing of his shirt from behind?

Joseph, peace be upon him, was imprisoned at the request of the wife of Al-Aziz to her husband after her affair became public and she told people that Joseph had solicited her. He was imprisoned to appease her and to silence people's talk, despite the clear evidence of his innocence. It was also said that she imprisoned him hoping that imprisonment would weary him and he would then give himself to her.