This is a purely geometric-based solution of light emitting from a source and spreading out in all directions and contacting another sphere some distance away. This does not account for any fancy "scientific" stuff that I am no expert at, such as the energy getting absorbed by the Earth’s atmosphere, or other factors that may be at work in this matter.
Here are some other sources I found that address some of the scientific issues of this matter, as well as other mathematical approaches to estimating this value:
Surface area of a sphere: A = 4πr^2
r is the distance of the Earth from the Sun = 92,960,000 miles (92.96 million miles)
Surface area of the "sphere" formed by this distance:
Area = 1.09×10 ^ 17 square miles
Cross-sectional area of a sphere: A = πr^2
r = radius of earth r = 3,958.8 miles A = 4.92×10 ^ 7 square miles
Divide Area of Earth by Area of Sphere:
(4.92×10 ^ 7) / ( 1.09×10 ^ 17 ) = 4.5137615e-10 = 4.5292×10^-10
For reference, "1 Billionth" is 1e-9, so 4.51e-10 is even less than this…
Basically, it’s "Less than 1 billionth"
It could also be stated as 4.5 "10 billionths"
= 0.00000000045137615 = 0.000000045137615 %