Failure events in a given systems are represented in a Sample space. For events E1, E2, E3,.... sample space can be represented as,

Sample Space = {E1,E2,E3,.....}

For example, if we take a car, the chance of car type failing or brake failure, AC failure all different events. All these are independent events.

Two events are independent if and only if,

P(A^B) = P(A) P(B)

Conditional probability is something where the events are dependent.