Lack of drives

It is common occasion that police officers and investigators see no motive for committing a crime and so they let the criminal go. Though, there is no crime without a motive. The lack of drives is a relative definition for motives that are unbelievable for investigators or unviable for them. Criminalists define three main groups of such hidden motives. Those are motives hidden in the past, replacing motives and inappropriate motives.
Motives hidden in the past are usually represented as some offence that took place years ago. It is possible that there were two friends who felt in love with the same woman. Say, she makes her choice in favor of one of them. Another one remains lonely with his offence. He is possessed with feeling of revenge, though he is not able to revenge for some reasons. With the lapse of time that desire grows and will be implemented few years later.
Replacing motives are usually common motives for serial murderers and maniacs. Say, there is a person who was offended by his mother. He loves his mother greatly and he can't hurt her, though he needs someone to revenge mother's cruel attitude towards him. In that case he chose women looking like his mother and implements his desire.
As you can see there for sure a motive for every single crime but sometimes it takes much time and efforts to find it. Though, it may be found in any case.