Ok, so I had the same problem... BUT with a different cause that others might be running into!
There's an error on the 'Pentax K-3 III Firmware Update v1.10 Released' page!
The error is caused by an old link in a link called
'from this page'! See below:
Pentax K-3 III firmware update instructions: - Download the firmware ZIP file from this page
The '
from this page link takes you to the *wrong* Pentax page - the page you're taken to is for downloading an update for the K-3 II - NOT for the K-3 III!
From my own experience I can say that when you attempt to update a K-3 III with a K-3 II update the camera just ignores the update and starts up normally without asking to apply the update.
For the record, the K-3 II update is called fwdc230b.bin. If you see that one, you're using the wrong link - assuming you're trying to update a K-3 III
As others have noted, the correct update is called fwdc233b.bin. That's the one you want if you're updating a K-3 III!
Make sure you use the link on the line: 'Download the K-3 III firmware from the
official Pentax firmware site.'