The probability of an impossible event is always $0$.

In probability theory, an impossible event is defined as an event that cannot occur under any circumstances. For instance, when rolling a standard six-sided die, the probability of rolling a $7$ is impossible since the die only features the numbers $1$ through $6$. Consequently, the probability of this event is $0$.

Probability serves as a quantitative measure of the likelihood of an event occurring, with values that range from $0$ to $1$. A probability of $0$ indicates that the event will never occur, while a probability of $1$ signifies that the event is certain to happen. Probabilities that lie between $0$ and $1$ represent varying degrees of likelihood. For example, a probability of $0.5$ suggests that there is an equal chance of the event occurring or not occurring.

When we label an event as impossible, we assert that there is no chance for that event to take place. This is why its probability is $0$. Mathematically, if we denote the probability of an event $E$ as $P(E)$, then for an impossible event, we have the relationship $P(E) = 0$.

Grasping the concept of impossible events is essential for effectively analyzing and solving probability problems. It enables you to swiftly identify and eliminate events that cannot occur, thereby simplifying your calculations and allowing you to concentrate on events that have the potential to happen.