The first hypothetical is not comparable to the original case because the person frozen on the ladder is still autonomous (albeit frozen in fear). To make it comparable you would need to change it to something like the following: the person had a stroke making it impossible for them to climb up down or even be helped and thus destined to die. The second hypothetical is a clear-cut example of self-defence and again not comparable to the actual case. To make this second hypothetical comparable it needs to be changed so that 1) both climbers have slipped and are incapable of saving themselves, 2) unless a third party intervenes both will die, 3) one climber is significantly heavier than the other and too heavy for the third-party to pull to the rescue and 4) their ropes are tangles in such a way that they only way the third-party can rescue the lighter climber is by cutting the rope to the heavier climber and expediting their death. In the case of the raft at sea, the sailors assumed a timely rescue was so unlikely that the weaker sailor death was all but assured. However, they assumed wrong - out and out murder. Finally, public outcry should have no bearing on sentencing.
The first hypothetical is not comparable to the original case because the person frozen on the ladder is still autonomous (albeit frozen in fear). To make it comparable you would need to change it to something like the following: the person had a stroke making it impossible for them to climb up down or even be helped and thus destined to die. The second hypothetical is a clear-cut example of self-defence and again not comparable to the actual case. To make this second hypothetical comparable it needs to be changed so that 1) both climbers have slipped and are incapable of saving themselves, 2) unless a third party intervenes both will die, 3) one climber is significantly heavier than the other and too heavy for the third-party to pull to the rescue and 4) their ropes are tangles in such a way that they only way the third-party can rescue the lighter climber is by cutting the rope to the heavier climber and expediting their death. In the case of the raft at sea, the sailors assumed a timely rescue was so unlikely that the weaker sailor death was all but assured. However, they assumed wrong - out and out murder. Finally, public outcry should have no bearing on sentencing.
Imagine the person who got pushed and undecidedly if destined to death or not was our close one, it's sad though
The trolley problem was never intended to have a clear-cut solution. Who'd want to be a judge!