From the other direction, this time; begin from the Law of Probability that would, if they were doing things in the right order rather than quickly, have been proven as the only possible Law that yields all of a collection of Law-fragments that would each have been motivated on their own.
The probability of an event is between 0 and 1:
\X. 0 <= P(X) <= 1
Definition: X \/ Y denotes "the event that X happens or Y happens or both happen".
Definition: X & Y denotes "the event that both X and Y happen".
Definition: ~X denotes "the event that X doesn't happen".
For every event, the chance that it both happens and doesn't happen is nope:
\X. P(X & ~X) = 0
And for every event, the chance that it either happens or doesn't happen is yes:
\X. P(X \/ ~X) = 1
If two events are mutually exclusive, in the sense that they can't both happen, the probability of either happening is the sum of the individual events' probabilities:
\X. P(X & Y) = 0 => P(X \/ Y) = P(X) + P(Y)
Keltham shall first pause and call upon them to recognize that Probability generalizes Validity; the laws of logical reasoning, that are valid over every possible world, can be seen as a special case of reasoning with the probabilities of 0 and 1.
He shall then, by way of illustrating some of what is being skipped over, ask them what bad thing would happen to them if they tried to claim that some events could have a probability of 3 or -7.