Assume besides Floating Watcher there are X other minions on the battlefield, so X+1 minions in total. If one damage is dealt randomly between all X+3 characters (the 2 players in addition), the probability for you being hit is Y:=1/(X+3) (Y defined as 1/(X+3)). The probability for you not being hit is (X+2)/(X+3)=1-(1/(X+3))=1-Y.
Now 9 damage are being dealt randomly between all characters. Since for every damage the target is chosen independently from the other damage targets the probability that you are hit by exactly A of the 9 damage is
(9 choose A) (Y^A)(1-Y)^(9-A)
which is the binomial distribution, where (9 choose A) is the binomial coefficient (Please look it up, calculator e.g. here).
The probability for you being hit 9 times is (9 choose 9) Y^9. Assuming there is no other minion on the battlefield except the Watcher, this is 0.00508 % (times 100 to get %).
The probability for being hit 0 times is (9 choose 0) (1-Y)^9. Assuming there is no other minion on the battlefield except the Watcher, this is 2.60122 % .
The probability for being hit exactly 4 times is (9 choose 4) Y^4 (1-Y)^5 = 126 * 0.16257 = 20.48468 % with no other minion on the battlefield.
If you want to know the probability for you being hit more than or equal to 4 times, you have to sum the probabilities for being hit exactly 4, 5, 6, 7, 8 and 9 times. This would be the same as the probability for the Watcher being dead if it does not get buffed during the resolution of Spreading Madness (Which I think is the case), since the probability for you or the Watcher being hit is the same. Please calculate yourself. :-)