PROBABLE CAUSE to arrest is defined as whether a police officer has objective, reasonable, and reliable information that the person under investigation has committed or was committing an offense.  There must be a probability of the commission of a crime, not just a possibility.  A probability is defined as more likely than not. 

For example, in the context of a DUI case, if a police officer smells alcohol on the breath of a person he suspects of driving under the influence of alcohol, and the person under investigation is staggering around, slurring his speech, as well as poor performance on "field sobriety" tests, the police officer has an objective and reasonable basis to believe this person has committed the crime of driving under the influence, and arrest is justified.