"must": obligation x certainty. Which meaning developed first in the English language?
Solution 1:
Historically, "strong obligation" (the deontic reading) arose before "certainty" (the epistemic reading). The deontic readings are attested in the earliest Old English texts, but the epistemic reading didn't arise until considerably after the Old English period.
In fact, the pathway of change from deontic to epistemic modality is a very common tendency cross-linguistically, and the reverse is said to be rare. Traugott (1989) has examples and discussion from the history of English.