Probability question with a definite outcome

So I'm having trouble calculating the probability of the following scenario:

I have 4 possible locations for 4 boxes. Each of these boxes may exist with a probability, β. There is also a circle, this circle definitely exists.There can only be one connection between the circle and the the locations of boxes (i.e. the circle can only be connected to one spots for the boxes). What is the probability that the circle is connected to a spot with a box which does not exist?

Attempt at solution:

So I figure that i would need to multiply the probability that there is only one connection by the probability that that box doesn't exist. The only problem is that I couldn't figure out which probability I am supposed to put in the binomial equation, because I can't put in (1-β) as p because then q would be β, but it doesn't matter to me that all the other boxes exist, all I care about is the box with the connection exists. And then I thought to put in the probability that there is one connection in for p, but then I got 1 and q is 0. So I am really not sure what to do...
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