To be arrested on DUI charges, the police generally need to have both probable cause and reasonable suspicion. Though these are similar, they are not the same. Typically, reasonable suspicion is involved in the initial traffic stop, while probable cause leads to the arrest. You can have one without the other.
A good way to think of it is by noting that reasonable suspicion just means the officer thinks you might have done something wrong. That can be reason enough to pull you over, but not to arrest you. Probable cause means the officer has some sort of evidence. While nothing has been proven yet, he or she thinks you most likely broke the law.
For example, maybe you're driving home and the officer sees you swerve in your lane. That could indicate that you might be drunk, and he or she can then pull you over. Reasonable suspicion has been satisfied.
When the officer talks to you, he or she gives you a breath test. It shows that your BAC comes in at 0.10. That's over the legal limit, so now probable cause has also been satisfied. The officer hasn't proven that you committed a crime -- the breath test could be inaccurate -- but he or she has reason to think that you probably did. You can then be arrested and head to court, where your true guilt or innocence will be decided.
It's very important to know all of your rights throughout this process. That's especially true if you think that police stopped you without reasonable suspicion or arrested you without probable cause.
Source: FIndLaw, "What is Reasonable Suspicion for a DUI Stop?," accessed April 21, 2017