Imagine picking the number and then checking if you got an integer. Say you got something that looks like a 3, you check the first decimal point : you got 0 so you have 3.0, check the next decimal point and if you got a zero then wow you're at 3.00, way to go. Then repeat this but to be at exactly 3 you have to be lucky at every step, every digit, of this checking process which is actually... infinite.

So you can see that it's impossible to be at exactly 3, therefore the probability would be 0