Pyth, 6 bytes

WQ=OQQ 

Try it online!

While Q is truthy, set Q to be a random integer between 0 and Q and print Q.

Not the shortest Pyth answer but I'm just learning and only posting because of the recent discussion about no-one using Pyth any more :)

Pyth, 6 7 bytes

QWQ=OQQ 

Try it online!

+1 to print the initial input value.

While Q is truthy, set Q to be a random integer between 0 and Q and print Q.

Not the shortest Pyth answer but I'm just learning and only posting because of the recent discussion about no-one using Pyth any more :)