When you get infected with SARS-CoV-2 (the virus that causes the syndrome called COVID-19), this virus will copy itself (=replicate) many times in cells of your upper and lower airways. After a few days after infection, the virus will be amongst others in your nose, that is why we test for a SARS-Cov-2 infection by taking a swab from the nose and often the back of the throat as well. Now as an experiment for yourselves; observe some people around you for lets say 20-30 minutes and count how many times they touch their nose with their hands.
I think that you will realize that, whenever someone is infected with SARS-CoV-2 and there is virus in the nose, the chance that at one point this person also has virus on his/her hands, is very big.
How big subsequently the chance is that this person infects other persons by spreading this virus with his/her hands I cannot tell you and is, as far as I know, currently unknown.