On a planet away and afar
Shines a Sun which to us is a star
     But only on days
     And according to ways
Of numbers and systems bizarre

Letting his light shine on (call it) day one
Then day two chances one percent dawn
     But if no light does shine
     Then a new day unwinds
And day three chances two percent Sun

So day four chances three percent Sun
If day three had also seen none
     And likewise it goes
     A generalization which shows
On day n chances n-1*

If the Sun shines on day one, then what day (or days) is most likely to also see Sun and what is the probability? (approximation to several decimal places is fine)

* n-1 percent ('Percent' does not rhyme with 'Sun' and 'none'.)