$4\mathrm{.}19$ Virus propagation

We start with a network of three computers. Unbeknownst to us$,$ two of the computers are infected with a hidden virus and the other is not. A sequence of new uninfected computers now join the network, one at a time. Each new computer joins the existing network by attaching itself to a random computer in the network $($all computers in the network are equally likely attachment points$).$ If the new computer attaches itself to an infected computer, then it immediately becomes infected with the virus; otherwise the new computer does not get the virus. At the point where the network consists of $k$ total computers, what is the expected fraction of these that is infected? Assume $k>3.$