Double century with a four Virat Kohli playing innings of his life. There are infinite overs. On each ball, he can score either 1, 2, 3,  or 4 runs with equal probability. What is the probability that he will score a double century with a boundary?
Rephrased version:A rabbit is at the bottom of the staircase with 200 steps, each time the rabbit can take 1,2,3 or 4 steps with equal probability. What is the probability that the rabbit will reach the 200th step with a step jump of size 4?
 A: BIG CAVEAT: These numbers are actually "infinitesimally close". See note below.
The probability is $\frac{1}{10}$.
There are two methods to see this.
First, we can calculate the probability of landing on 196 by a long iterative process that is easily done in a spreadsheet. 
The probability of starting at 0 is 1.
The probability of landing on 1 is $\frac{1}{4}$.
The probability of landing on 2 is the probability of rolling there from zero directly ($\frac{1}{4}$) or of hitting one and then rolling a 1 ($\frac{1}{16}$).
We can continue this process until we get to four, where we can simplify it as $\frac{1}{4}$ times the sum of the previous four rows.
If we do this formula and then repeat it down to 196, we see see that very quickly, the probability of landing on any given number is $\frac{4}{10}$. If we land on 196, we have a $\frac{1}{4}$ chance to roll a 4 and fulfill the conditions. Thus, $\frac{4}{10}\frac{1}{4}=\frac{1}{10}$.
Second method:
Let us assume we hit 200 or went over after this process and examine the pairs (previous number, final roll): {(196,4),(197,3),(197,4),(198,2),(198,3),(198,4),(199,1),(199,2),(199,3),(199,4)}. There are ten of them, and I argue that they're equally likely. 
NOTE ABOUT "CLOSE": The probability of each step is not actually 0.4. It is very close. The probability of hitting 0...4 is $1,\frac{1}{4},\frac{5}{16},\frac{25}{64},\frac{125}{256}$ respectively. They then start approaching 0.4 as a limit.
