Consider a cybersecurity scenario involving malware detection on a computer network. Suppose we have a network with $1000$ computers, and we know from historical data that $10\%$ of these computers have vulnerable software that could potentially be exploited by malware. Additionally, let's say that there is a particular type of malware known as "Malware X$,"$ which has been observed to target vulnerable software with a probability of $5\%.$

If we randomly select a computer from the network, what is the conditional probability of that computer being infected by Malware X$,$ given that it has vulnerable software installed?

the answer, the calculus, and a explanation of your solution $($calculus$).$

please please dont use Ai tools answers by human logic.