In A Galaxy Far, Far Ago

Lurk Skywalter is exploring the planet Tantoone with his robot friend, WD-40, when he sees a figure off in the distance. He forgot his glasses, though, so he is not sure whether the figure he sees is a swamp rat or his good friend, Hans Sorbo (the captain of the famous spaceship Millionaire Falcon).

Lurk has a simplified worldview, wherein the world consists of five discrete locations, numbered as shown below:

Over the years, Lurk has built up a detailed model of how swamp rats and Hans move through the world:

1. Every minute, Hans has a probability 0.4 of moving one cell to the left, and a probability 0.6 of moving one cell to the right.

2. Every minute, a swamp rat has equal probability of moving to any cell, regardless of where it started.

At 12:01pm, Lurk knows with 100% certainty that the figure is in location 2. He thinks the figure looks only a little bit like a human, so he decides that, with probability 0.25, the figure is Hans; and with probability 0.75, the figure is a swamp rat.

At 12:02pm, after the figure has moved, Lurk knows with 100% certainty that it is in some location n.

For what values of n, if any, would Lurk become completely certain that the figure is a swamp rat?

Enter a list of numbers (if the answer is none, enter an empty list): 

For what values of n, if any, would Lurk become completely certain that the figure is Hans?

Enter a list of numbers (if the answer is none, enter an empty list): 

For what values of n, if any, would Lurk become 50% certain that the figure is a swamp rat, and 50% certain that the figure is Hans?

Enter a list of numbers (if the answer is none, enter an empty list):