Why did the battles of Lexington & Concord give the colonists hope?

The battles of Lexington and Concord were the first military engagements of the Revolutionary War. Though the colonists didn't win, they proved to themselves and to the British that they were more than capable of standing up to what, at that time, was the largest and most powerful fighting force in the world. During both battles, the colonists showed considerably more bravery than military skill. For instance, American marksmen sustained a higher percentage of casualties than their more numerous redcoat opponents.
But in the overall scheme of things, this didn't much matter. The main significance of Lexington and Concord was political rather than military. The fact that the Americans had gone toe-to-toe with such a mighty army was a huge morale boost which the colonists desperately needed to encourage them to go on fighting. Prior to these engagements, even some of the most patriotic Americans were skeptical as to whether or not they could carry out sustained armed resistance. But in the aftermath of Lexington and Concord, such skepticism virtually vanished overnight. The Americans had shown that they could fight, and there was to be no turning back.