Some doubt still remains about his explanation.
警察は彼に殺人の疑いをかけている。
The police suspect him of murder.
There is no doubt that he is the culprit.
She had doubts about the story.
Unnatural behavior invites suspicion.
疑い is the plain, everyday word for suspicion or doubt, while 嫌疑 is a formal term reserved for legal or investigative contexts.
疑い is the plain, everyday word for suspicion or doubt, whereas 懐疑 carries a more formal, reflective, philosophical tone.