Explanation
In probability theory, a conditional probability is the likelihood of an event occurring given that another event has already occurred. This is denoted as $P(A \mid B)$, which reads as the probability of $A$ given $B$.
Key Formula:
$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$Where:
 $P(A \mid B)$ is the conditional probability of event $A$ occurring given event $B$.
 $P(A \cap B)$ is the joint probability of both events $A$ and $B$ occurring.
 $P(B)$ is the probability of event $B$ occurring.
Given Situations
 The probability that your team wins the championship given that you go to the finals is a conditional probability because it is based on the condition that you have reached the finals.

The probability that you are given a bike for your birthday is simpler and is not based on another event. Hence, it is not a conditional probability.

The probability that you roll a 1 on a number cube is an independent probability event and doesn't depend on any prior condition, so it is not conditional.

The probability that your team wins the championship generally, without any extra information, is not conditional since it doesn't depend on another prior event.