Imagine, for example, a 5x5 grid of cards, face down. The cards are either red or blue. Someone has given you the number of red cards for each specific row and specific column. Thus--focusing on a single row or column--if you picked a card at random from that row or column, you would know the likelihood of the card being red; if there's only 1 red card in a given row, the chance that you'll select a red card will be 1 in 5 or 0.2, and if there's no red cards in a given column, the chance that you'll select a red card will be 0 in 5 or 0.
How then, would someone calculate the probability of a specific card being red, being that the card is on the intersection of a row and column, each of which have a known probability?