This is where I would start. I would first get X and Y to be similar units i.e. convert Y from average in seconds to average in hours.
Then I would multiply X and Y to eliminate hours.
From there I would divide XY by Z.
X = 100 connections/hour
Y = 360 seconds
Z = 50 connections
Y = (360 seconds)*(1 hour/3600 sec) = 1 / 10 hours
XY = (100 connections/hour) * (1 / 10 hours) = 10 connections
XY/Z = (10 connections) / (50 connections) = .2 = 20%
This probably isn't the best solution for this problem, but in my mind this is an acceptable one. I feel like more information (i.e. standard deviation and variation) would help give a better and more accurate probability.