From the law of the burglar, the Mekhilta derives one of the most important principles in Jewish law: a doubt about whether a life is in danger overrides the Sabbath.
The reasoning is an a fortiori argument of extraordinary power. Consider the act of killing. Taking a human life defiles the land and causes the Shechinah — God's divine presence — to depart from Israel. There is virtually no graver act in all of Jewish law. Yet even this most severe of actions is permitted when there is merely a possibility that one's life is at risk. The homeowner is allowed to kill the intruder based on doubt alone.
If killing — the most extreme act imaginable — is overridden by a possibility of saving a life, then surely Sabbath observance — which, however sacred, does not carry the same gravity as homicide — should also be overridden by a possibility of saving a life.
This principle became one of the pillars of Jewish medical ethics. A doctor who is unsure whether a patient's life is in danger does not wait for certainty before acting on the Sabbath. Uncertainty is enough. The Mekhilta established that the standard for overriding Sabbath is not proof of mortal danger but the reasonable possibility of mortal danger. Doubt saves lives. And saving lives outranks everything — even the holy Sabbath that God Himself observed at the dawn of creation.