。
The light's on, so he must be home.
Literal
Light [subject-が] on-is [because-から] he [topic-は] house [at-に] exist [must-に違いない].
に違いない = 'must be, no doubt about it' — a strong assertion of probability based on evidence. Literally 'there is no differing.' Stronger than だろう or はずだ. Used when the speaker is certain based on reasoning.