This petty little business, as you call it, bears directly on a very big business, bigger perhaps than either you or Miss Tuppence know.
The business is a serious one that neither your nor Tuppence could know. 
mnli hypothesis: The business is a serious one that neither your nor Tuppence could know.  premise: This petty little business, as you call it, bears directly on a very big business, bigger perhaps than either you or Miss Tuppence know.