The probabilities:
-Two break points are selected randomly (and distributed uniformly) on the stick.
The stick is first broken into two pieces. The longest (or rather, not the shortest) is then broken into two.
-The stick is first broken into two pieces. A piece randomly selected with probability 1/2 is then broken into two.
-The stick is first broken into two pieces. A piece randomly selected with the probability proportional to its length is then broken into two.