Conditional Probability vs Probability

Conditional probability updates the chance of an event once you know another event has happened. It is written $P(A \mid B) = \frac{P(A \text{ and } B)}{P(B)}$ (the probability of $A$ given $B$), the probability of both divided by the probability of the given event. For example, if 40 percent of students take both Spanish and art and 50 percent take Spanish, then the chance of art given Spanish is $0.40 / 0.50 = 0.8$. Restricting attention to $B$ is what given means.

Probability measures the long-run relative frequency of an event over many repetitions. For equally likely outcomes, $P(A) = \frac{\text{number of outcomes in } A}{\text{total number of outcomes}}$. For example, rolling an even number on a fair six-sided die has probability $3/6 = 0.5$. Over many rolls the fraction of even results settles near this value, an idea called the law of large numbers.