To come to your home and arrest you, the police typically need a warrant. To get that warrant, they need to have probable cause. They'll go before a judge, show him or her what evidence they have and why they think an arrest needs to be made. Then, with that in hand, they'll come and make the arrest.
However, a warrantless arrest can also be made. This is common when a police officer witnesses a crime -- or thinks he or she did, at least -- or when others may be in danger if the arrest is not made quickly. It can also happen in situations where there is no time to go get a warrant, such as when a person is pulled over on suspicion of drunk driving.
If this happens to you, it is generally still legal, but only if the police can show after the fact that probable cause did exist. They don't get around this requirement just because they did not get a warrant first. Rather than demonstrating that they have reason for the arrest beforehand, they must demonstrate it afterward, or the arrest could be deemed illegal and prosecution will not continue.
For example, police can't just arrest drivers and bring them in, assuming they're drunk and giving them breath tests at the station. They need to see probable cause just to pull the car over -- such as swerving out of the driving lane -- and then they need a reason to suspect the person is really drunk, such as a failed field sobriety test.
If you have been arrested in Denver and you don't believe the police had cause to do so, your rights as a citizen may have been violated. It's crucial that you know how this violation may get your charges thrown out of court.
Source: FIndLaw, "Probable Cause," accessed Oct. 14, 2016