Conditional probability is the probability of an event given that another event has already happened. The notation $P(A \mid B)$ means "the probability of $A$ given $B$".
$$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$$
In practice, most GCSE questions are solved using a two-stage tree diagram where the probabilities on the second set of branches change depending on the first outcome (sampling without replacement).
Example: A bag has 5 red and 3 blue counters. Two are drawn without replacement. Find the probability that both are red.
$$P(\text{red then red}) = \frac{5}{8} \times \frac{4}{7} = \frac{20}{56} = \frac{5}{14}$$
The second branch changes to $\frac{4}{7}$ because one red counter has been removed.
Common error: using the same probabilities on both sets of branches — always update the denominator (and numerator if appropriate) after the first draw.