If I am 80% sure, is there an 80% chance that I'm right? A friend of mine said this, and I couldn't argue why I thought it was wrong.
Obviously, in some circumstances it is valid, say if you flip a coin, and I say I'm 50% sure it lands on heads.
In a discussion about whether sending a "dick pic" was illegal, he said:

I'm 99.3% sure, so there's only a 0.7% chance that I'm wrong.

Now, if we assume that it is illegal, I would agree, but isn't there a 50% chance that there is a 99.3% chance that he is wrong?
Could someone explain to me if and how this is wrong?

I think the main problem here is that "he is sure" is something else than "he is right". He might be 100% sure but still dead wrong, while when there is a 100% chance that he is right, then he is right.  
In the sentence you highlighted, he is assuming that his being sure is equivalent to his being right. Of course, a sentence like 

The chance that I am right is 99.3%, so there is only a 0.7% chance that I'm wrong.

is completely correct, but he doesn't know the chance that he is right, he just gives some random, high number to convince you.
