The Smith and Wesson model K14-3 was produced from 1947-1982. You would need to write into Smith and Wesson with the model and serial number. They can pull the date and send it back to you.
Your question cannot be answered without you providing the serial number to your model 586 Smith and Wesson revolver.
You can not tell the model number with just the serial number.
You can not determine the exact model with just a serial number.
With the brief description that you have supplied,I would say that you have a SMith and Wesson model of 1905 4th change revolver.
No way to answer without the serial number.
Impossible to answer with the information given.
behind the celinder
If the serial number is J75635 then your Smith and Wesson model 36,J frame revolver was made between 1979-1980.
Your serial number of 3K62917 indicates that your Smith and Wesson model 14-3 was made in the year 1972.
Can't tell model number from just the serial number.