What is this error dns_probe_finished_no_internet and how can i fix it

You can fix DNS_PROBE_FINISHED_NO_INTERNET error in Google Chrome By Applying This Method:
Open Command Prompt (Run as administrator) in your PC.
Type the following code and hit enter...
netsh winsock reset
Now simply restart your PC and error must be resolved now....
Source: DNS PROBE FINISHED NO INTERNET

I found this guide from Google which was helped me to fix the same issue.

I would recommend you try it to help you fix dns_probe_finished_no_internet error.

Fix DNS Probe Finished No Internet Error In Google Chrome

This error means no internet, i would sugest followign steps below to fix this. BEST FIX DNS PROBE FINISHED NO INTERNET

Ouch. Are you one of those poor guys on Lucas Internet? Sorry, I meant to say Daemon. :)
Assuming your broadband light is on (WAN Link) and you have access to the administrative interface and that's where you see the message either the connection is down or your 582 needs a good old fashioned power cycle reset. If that doesn't bring it back, and you can't contact your ISP to see if there is an outage in your area you might try a factory reset (with the reset button on the back) I DON't ADVISE doing a factory reset, unless you have all your account information handy, just offering it as an option.

It has tried to find the internet connection and failed.

Look at you internet cable and whether the cable modem etc. is working.