A single bacterial cell, which would have to be magnified over a million times to even be visible, contains 100 billion atoms. I think you see where this is going. Life is exceedingly improbable. But low probability by itself is not enough to force an inference to design. The precise distribution of atoms in a given snowflake is extremely improbable, because all snowflakes are different and there are many of them.
Snowflakes are also highly ordered and possess a somewhat complex, specified structure.
Order is greatly valued in science, and rightly so. The structure of snowflakes, while the probability of the exact conformation of each individual flake is quite low, is the infallibly predictable result of matter obeying the laws of chemistry and physics under certain conditions. Snowflakes, then, although low-probability and specified, are also low in information, because their specification is in the laws, which are always and everywhere the same. So now we have discussed chance, the very opposite of design, and law, which results in some design, although it's endlessly redundant, and has low information content. A page filled randomly with letters of the alphabet is a low probability event.