The countability of the set of all Turing machines

Question

There are many questions like this but I couldn't find what I was looking for in them. I already know that the set of all Turing machines is countably infinite but I couldn't find a proof of this, also it doesn't make sense to me intuitively. So, my question goes like this: In the book it says that we can encode Turing machines as strings and somehow this makes it countable. I understand that this statement is true if the alphabet of those strings is finite or countably infinite(I am not really sure about this one). what happens if the alphabet is uncountably infinite? or why can't it be so?