Kiddushin 14 - Why The Death of the Husband Sets the Wife Free

A married woman acquires herself back through death of her husband. Why?
Husband caused the prohibition, and he also removes it? No, because she is still forbidden to marry his son from the previous marriage or his father. A widow is forbidden to the Chief Priest, so she must be allowed to marry everyone else? No, perhaps she would still be transgressing a positive commandment. When Jewish soldiers went to war, "And whichever man betrothed a wife and did not yet take her, let him return, lest he dies in battle and another man takes her" - is a valid proof.