He decided that Tuppence, in the throes of anxiety, had gone to the police, and that his disappearance having been made public the gang had not been slow to put two and two together.
Tuppence was content and lacked worry and didn't leave the house. 
mnli hypothesis: Tuppence was content and lacked worry and didn't leave the house.  premise: He decided that Tuppence, in the throes of anxiety, had gone to the police, and that his disappearance having been made public the gang had not been slow to put two and two together.