You failed to explain your use of the word "suspect". What are they suspected of, being a potential criminal? In stop and frisk, that is the case.
If an actual crime has occurred, then you can talk probable cause for chasing a "runner".
NYC ain't Mayberry - it's a city of 8m people. There are outstanding warrants against all kinds of people and cases involving tens of thousands of property crimes that aren't even investigated. There's no question that crimes have occurred, continue to occur and will occur within minutes of anything they do - the only question is who they can make for those crimes.