Let a denote A works, and -a denote A fails and similary for the other systems. Also let t denote that Thorhead works and -t that it fails.

P(-a|-t) = P(-a)P(-t|-a)/P(-t)

this is Bayes theorem where P(u|v) is the conditional probability of u given that v has occured. By definition here P(-t|-a)=1, so we have:

P(-a|-t) = P(-a)/P(-t) = (1/3)/P(-t)

Note P(-t) = 1 - P(no systems fail) = 1 - (2/3)^5, so:

P(-a|-t) = (1/3)/(1-(2/3)^5)

RonL