Chess board probability problem. Three random squares are chosen from a regular chess board. Find the probability that they form the letter 'L'.
I cannot think about a general way to go about these type of questions. Need hints or solutions.
Note: I'm assuming that an "L" is three squares that fall in a $2\times 2$ box. If you want the sides of the L to be able to have any size, please clarify.

Why don't you try counting the number of $L$s that are possible? We can count the number of "successes" (the number of times three squares form an $L$) and divide that by the number of ways to choose three squares.

If we fix a direction on the chessboard as "up", then there are four orientations our $L$ can take. By symmetry, there are the same number of ways to make each $L$, so let's count the ones that are oriented the way the letter $L$ usually is. If we think of an $L$ as being a $2\times 2$ box with one square removed, we are looking at the case where the upper right square is the one removed.

The location of the $L$ is uniquely determined by the location of the lower left square. This square can be placed anywhere except on the right-hand column or the top row, as that would cause the $L$ to not fit on the chessboard. Thus there are $7\cdot7=49$ ways to place the $L$ in the orientation we have chosen. There are four orientations, so the total number of $L$s is $4\cdot49=14^2=196$

You don't specify how the squares are chosen, but if we assume you want to choose three squares uniformly at random, there are ${64\choose 3}$ ways to do that, since there are $64$ squares on a chessboard. Since I'm assuming every choice is equally likely, the ratio of these two numbers is the answer: $\frac{7}{1488}\approx 0.0047$ or a $0.47\%$ chance.
There is a 1.92 % chance of making an "L" without space in between. If you mean that they can form an "L" when they are far from each  other is a different story.

POSSIBLE Solution: 64/100=0.64    0.64x3=1.92,
And this was in percentage form. If you need the answer not in percentage and in something else i can`t help you right NOW.