Probable cause is the level of proof that is needed before a warrant can be issued for an arrest or a search.
Probable cause can be defined as facts or evidence that would be sufficient to convince a reasonable person that a crime is being committed, that it will be committed, or that it has been committed (and that a given suspect is responsible).
There are two important aspects of this definition. First, there need to be facts or evidence. Probable cause cannot exist on the basis of a hunch or a guess. Second, the evidence needs to be sufficient to convince a reasonable person. There does not have to be proof beyond a reasonable doubt. On the other hand, it has to be proof enough to convince a reasonable person, as opposed to someone with a grudge against the suspect or someone who is paranoid.
Although it is not easy to define in an exact way, probable cause is one of the most important concepts in our system of criminal law.