Random Within Random Probabilities

I fancy myself a programmer, and I've created a bit of code including a randint(randint(1,6),6). For those of you who don't speak the same language I do, it basically finds a random integer from 1 to 6, and then finds a random integer from that number and 6 again.

Once I got done with the bit I was using it for, I got curious as to the probabilities of it returning certain numbers.

I tried doing some simple math in my head, but my brain kept throwing in the fact that there is no such thing as true randomness in programming, and my math kept getting super complicated, and ultimately wrong. So I googled for a math help forum and came here.

Can anyone tell be the probabilities of my formula returning each number from 1 to 6?