Example:
When you toss a coin, there are two possible outcomes in the sample space, S. If we believe the coin is balanced, then we assign 1/2 for each possible outcome.

P(H) = 0.5
P(T) = 0.5

If we believe the coin is unbalanced, we might assign something like:

P(H) = 0.4
P(T) = 0.6

The sum of the probabilities getting heads or tails, however, is equal to 1. The probability of getting a head in a coin toss is not necessarily 1/2. Some coins are unbalanced! If an event is certain to occur, its probability is 1. If it is certain not to occur, its probability is 0. For example, the probability of drawing a King of spades from a 52 card deck is 1/52. Since a Red King of spades does not exist, the probability of drawing a Red King of spades is 0.

When there are more than two possible outcomes, the sum of the probabilities is still equal to 1.

Example:
Suppose that there are 10 candidates running in the next election. Without knowing about any of them, you would suppose each has an equal chance of winning. Since the total probability must equal to 1, the probability of winning for each candidate will be 1/10. This can be summarized in the table below:

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10) = 1