When the defendant seems like the only person who has a motive, the jury will usually convict him or her on the basis of there being no one else who would have likely done it. A defense attorney needs to be able to demonstrate that there is solid evidence that the crime was committed by another person, something which is known as the alternative perpetrator strategy.
In the case of Amy Allwine, her life had been threatened six months before her death and all the evidence at the time pointed to it being a fellow dog-trainer, not her husband, who had gone online to a dark web hitman site.