UNO's digital pin continue to read 1 for a while
Digital inputs should either be low or high. In this image acceptable input voltages on the left represent common TTL voltages based on a 0 to 5 volt range:


It is bad practice to leave a digital input floating.  A floating or disconnected input implies the voltage is unknown.  I suspect in your case a small amount of input capacitance held a charge for several seconds.  Once leaked off the input appeared to change from 1 to 0.  Even though you know what might be happening, you should not depend on it as it is unreliable behavior.

If connecting a SPST switch use a pull up (or pull down) resistor to pull the input pin to the opposite voltage the switch is pulling.  In this image the switch is connected to ground so the resistor is connected to positive voltage as a pull up:



The fist image comes from this Logic Level tutorial.