Having no idea what year your street triple is, I can only suggest a quick check that the clutch safety switch is firmly locked in place on the clutch perch. If the switch backs out the ECM will be messed up and a very low idle is one of the results.
This was a problem I had on my '08 1050 Sprint. A 675 ECM might work the same.

 

It's a 2008 street triple.

 

Make sure the little rubber tube to the manifold pressure sensor at the bottom left of the airbox is connected to the bottom of the sensor. Make sure the air filter is clean and the various hoses connected to the airbox. Also NEVER shut off the running engine using the 'kill' switch or attempt to start the engine with the 'kill' switch on. Spray all the interlock switches and switch-gear with WD40. If the ECU tune is a bit messed up the best thing to do is have the dealer re-upload the most recent map for your VIN number (and exhaust system) and do a proper TPS or 'adaption' reset.

 

The MAP sensor tube will cause this...just happened to mine a few weeks ago...it simply came off.

 

Does the MAP sensor tube go by another name? I can't find reference to it in my Haynes manual!

 

Just find the Map Sensor, and then see if there is a rubber vacuum tube still connected to it underneath it...check to see if it's kinked, split or just off the sensor.