Derivation of time probability distributions for single molecule kinetics
To see how this calculation is done, let us consider the simpler case of just the second step shown above, ie $\ce{AB -&gt;[k_{f2}] C}$. Since we are interested in the situation where no $C$ has yet formed, the reverse reaction can be ignored. I will assume that this reaction is first order in $AB$, so $k_{f2}$ has units of $s^{-1}$. 

In this case, the rate constant $k_{f2}$ represents the average frequency of the reaction. 

Now let's consider that we establish an infinite number of evenly spaced time intervals of length $\Delta t$. When we consider the probability distribution, we need to consider two factors:

1) The probability of reaction occurring in an interval $t_n + \Delta t$ and

2) The probability that the reaction has not yet occurred at $t_n$

The first value is simply the product of the rate constant $k_{f2}$ and the length of the time interval: $k_{f2}\Delta t$.

The second probability is slightly more complicated, since it is the chance of the reaction $not$ occurring in each of the $n$ intervals preceding $t_n$. That probability is given by $1-(k_{f2}\Delta t)^n$. Conveniently, as our time interval $\Delta t$ goes to $0$, this probability becomes a continuous function $e^{-k_{f2}t}$.

To get our final probability, we simply multiply these two probabilities:

$[\text{total probability of reaction occurring in interval }t+dt] = [\text{probability of occurring in interval }t+dt] \times [\text{probability that reaction has not occurred by time }t]=k_{f2}dt\times e^{-k_{f2}t}$

The probability as a continuous function of $t$ therefore can be written as 

$p_{\ce{AB-&gt;C}}(t)=k_{f2}e^{-k_{f2}t}$.

As expected, integration from $t=0$ to $t=\infty$ gives an overall probability of $1$.

Reference: Adapted from the lecture notes published by Dmitrii Makarov here: http://makarov.cm.utexas.edu/resources/Lecture-notes,-tutorials-etc./single-vs-bulk.pdf

For the two-step process, if $\ce{A+B &lt;=&gt; AB}$ establishes equilibrium very fast relative to the $\ce{AB-&gt;C}$ reaction, then the above is a reasonable approximation (after adjustment of $k_{f2}$ to reflect the equilibrium concentration of $AB$). If the equilibrium is not established quickly, then you would use the same reasoning to determine the probability first of $AB$ having formed by time $t$ and then the probability of it reacting based on how long it has been in existence. 

I have not read Makarov's textbook on single molecule kinetics, but I assume it covers these kinetics in much greater detail and might be a good resource:

Single Molecule Science: Physical Principles and Models
1st Edition by Dmitrii E. Makarov; CRC Press 2015; ISBN 9781466559516