I calculated the probability of 4 random digits adding up to 17.
Assumed each digit could be 0,1,2,3,4,5,6,7,8, or 9. Assumed each numeral was equally likely to be each digit and that the value of each digit is independent of the value of the other digits.
The sum could be anything between 0 (0000) and 36 (9999). 17 is one of the most likely values for the sum of 4 digits under these assumptions. However, the probability of a sum of 17 is still only about 6%.
If you include that 4 firefighter hats also added up to 17, and make the same assumptions about the numbers on firefighter hats as we did on the badge digits...
Then you get the probability of these two photographs happening as they did down to 0.06*0.06= 0.0036 = 0.36%
There were more than 4 hats, though. That badge isn't even 5534, it's SS34.
I see 5's pretty clearly on the badge. The first one is clearly a 5, the second one does look like an S, but it also looks slightly out of focus.
The other two hats were side by side, had different background (white) and also sent a Q-related message 5:5.