The OP mentioned in another comment that the draw is once a year

Also, it's 0.005 increase in the chance per day. If you start from zero, then 0*1.005 is still zero. Even after 100 years, still zero.

But let's assume you start from 0.005, then the next day your chance would grow to 0.005*1.005=0.005025. it'd take extremely long for the chances to be reasonable