。
You heard the story, so you must be interested.
Literal
Story [object-を] heard [because-のだから] interested [supposed-to-筈だ].
A deductive inference made explicit. ~のだから ('because, given that X') is stronger than plain から — it presents the preceding clause as established ground for the next inference. 筈 (はず, often written in hiragana) is the noun for 'expected state,' 'what is supposed to be the case' — ~はずだ means 'it should be the case that X,' 'X is supposed to be so,' 'X must be true (by deduction).' Distinct from ~に違いない (subjective certainty) and ~だろう (guess): はず is deductive, 'it follows from what we know.' A classic syllogism-in-miniature.