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900 possible outcomes, 

ones that have at least 1 zero: every ten and 100-109,200-209,300-309,...900-909

900/10 = 90

90+90=180

would this be right?

Notice that  in each hundred....we have  [ 10 + 9 ]  =   19  integers that contain at least one zero

And there are  9 "blocks" of  "hundreds"   from  100 - 999

So.....the probability  is :

[ 19 * 9 ]  / [ 999 - 100 + 1 ]  =   171 / 900    =  [ 19/ 100 ]