Is a divorce effected by the husband's statement to his wife: "If you leave the house, you are divorced," without specifying a time, and then she leaves three days later and he is agreeable, knowing that this is the final divorce? And is a divorce effected by permanently preventing the wife from leaving?

A conditional divorce takes effect if the condition it was contingent upon is met. Thus, your wife's departure from the house triggers her divorce. If you did not qualify the wording or the intention, then your wife would be divorced every time she leaves, leading to an irrevocable major divorce (baynunah kubra). Some scholars hold that if a conditional divorce was intended as a threat and not an actual divorce, then an expiation for breaking an oath (kaffarat yamin (definition)) is required when the condition is met. It is advisable to consult a Sharia (definition) court.