It depends on what legislation affects the private sector.
Say the private sector can turn away people with genetic defects and the like, that is specifically those more likely to have larger medical bills throughout life or people who are already chronically ill.
Or say they can turn away daredevils who do lots of snowboarding or whatever sport gets you hospitalised most.
If private insurance then holds 60%, it will result in the 40% percentually holding more of the high cost individuals, thus increasing costs for all those paying their share.
If this is however prevented via legislation, then private health insurance companies holding 60% will only affect the remaining 40% via statutory health insurance instances still having costs that don't go down with less people to keep track of in their system.
For example the members of the IT staff still need to be paid for keeping the network running, servers & thus privacy of the citizens secure, develop the website and will normally still be needed as much as before for these tasks.
But the question is, of course, how much this actually will amount to.
That said this question and this answer can really be equated to a typical red herring. In reality the sum of many more questions and answers is needed before one can estimate the reality of private vs statutory health insurance.