Three distinguishable balls are distributed in three cells. Find the conditional probability that all the three occupy the same cell, given that at least two of them are in the same cell.

Since each ball can be place in a cell in three ways. Therefore, three distinct balls can be placed in three cells in 3×3×3 = 27 ways.

Consider the following events:           

E = All balls are in the same cell.

F = At least two balls are in the same cell. 

All balls can be placed in the same cell in three ways.