By definition it would never become infinite, that's just what it'd be; there could be no point of becoming.
To tackle it from another angle, my cousin, who has a degree in mathematics, explained to me, there are infinities of different sizes. There is an infinity between the numbers one and two because numbers are infinitely divisible. So there's no need for conversion between finite and infinite: the two are part of the same system.

The OP assumes that knowledge must always be correct or 'true' knowledge. This isn't necessarily the case. The best definition that I can think of off hand is that knowledge is any part of a worldview.

It means that we don't know whether they will or they wont buy ice cream.