If probability of event happen is 1 out of infinity is it possible to happen?

Yes. In fact for a unique event it could have already happened.

The ratio 1:infinity is, practically speaking, identical to a probability of zero.

This is because there is *literally* an infinite number of possibilities other than that 1.

Consider the ratio and the corresponding probability:

1:1 - probability 50%

1:10 - probability 9.1%

1:100 - probability 0.99%

1:1000 - probability 9.99 x 10^-2%

1:10000 - probability 1.00 x 10^-3%

etc.

The probability keeps getting smaller, at this point an onward by a factor of 10 with each step.

Now, carry that series out infinitely. The probability becomes - literally - infinitely small. "Infinitely small" is, practically speaking, zero. (You can't get smaller than zero when restricted to positive numbers.)

Yes it is possible to happen. It's just the probability of it happening keeps decreasing because numbers keep going.