why does aristotle insist on the law of probability and necessity with respect to all elements of tragedy?

The law of probability in terms of tragedy simply means the probability that a given character will react to a given situation is high because of human nature. Aristotle argued that the 'Universality' of human nature dictates the probability of a character's reaction in a specific circumstance,

"A character must act in accordance with human nature - either through probability, i.e. what 'most of us' would do, or through necessity, i.e. what we are 'forced' to do. An action cannot seem arbitrary - otherwise not only will it violate the determinate structure and break unity, but it will also irritate an audience that sees no basis for the action in human behavior. "

So, for example, when Horatio sees Hamlet (and just about everyone else) dead at the end of the play, his immediate reaction is to kill himself. Suicide is a probable and plausible idea for Horatio to think about given the circumstance.