Without a shadow of a doubt = it is absolutely, without question, certain, it will definitely happen!
"Yes dear, without a shadow of a doubt, i will make it to our dinner tonight."
" Miss dad's birthday party? No way, without a shadow of a doubt, I will be there."
"Do not call the repairman, I know how to fix it and i will. It's beyond a shadow of a doubt."
It is often used because past history indicates the person might not actually arrive or make the " thing" happen.