This animation shows the changes in liquid content within the first two potato halves.
The graphics below explain the non-appearance of liquid in the other two cases:
In the case of the 3rd potato half, there is no solute to start the process off so the cavity remains dry.
The 4th (boiled) potato half has had its cell membranes disrupted by the boiling process, so water does not pass from cell to cell by osmosis.
