Assuming that in the multiplication of bacteria by fission (division into two bacteria) the probability of a bacterium dividing during a time interval \(\Delta t\) is equal to \(a \Delta t+o(\Delta t)\) and is not dependent on the number of previous divisions or on the number of bacteria present, find the probability that if at time 0 there was one bacterium there will be \(i\) bacteria at time \(t\).