Below is a mathematical proof that miracles can occur and a calculation of their probability.

any finite number divided by 0 = infinite

so 3 / 0 = infinite

which can be rearranged so

0 x infinite = 3

if a miracle is defined as something with probability 0 (ie it is impossible and would require divine intervention to occur) and we assume the universe is infinite in either time or space or both.

the expected number of success of n trials is the number of trials x the probability of success (eg if you threw a dice 12 times you’d expect 2 sixes). So if the universe is infinite then there are infinite trials and if a miracle if a miracle has probability 0 the expected number of miracle = infinite x 0 and as shown above this equals 3.

so to recap

3/0 = infinite

so 0 x infinite = 3

p(miracle) = 0

E(miracle) = n p = 0 x infinite = 3

so in all of time and space 3 miracles are expected. However as any finite number divided by 0 = infinite then all we can say is that in all of infinite time and space a finite number of miracles are expected.

From this we can calculate the probability of one miracle occurring using the poission distribution

if X = number of miracles

X ~ P_o(3) as above

P(X = 1) = (e^-33¹)/1! = 0.0498 x 3 = 0.149

So there you go, when the universe is infinite

The probability of a  single miracle is 0.149

or

P(miracle) = 0.149