A "strong hunch" means having a very strong feeling or intuition about something, even though you might not have concrete evidence or proof to support it. Full definition
ART DIRECTOR TARA KLEIN: After my favorable impressions of the current Hyundai Sonata and Elantra, I had a pretty strong hunch that I'd like the Veloster. (autoweek.com)
Think of what I am going to tell you as merely strong hunches of mine which I have stumbled upon over the course of 21 years. (fundooprofessor.wordpress.com)
And I also have a pretty strong hunch that they're thinking pretty seriously about tablet form factors as well, maybe with a detachable keyboard. (recode.net)