where's the white king?

in case the above doesn't work:

W: K??, Ba4
B: Kd1, Rb5, Bd5

Black to move, but where is the white king if this is a legal position?

The answer is c3.

Quite a famous puzzle.  Here's this sequence (yes, I've seen it before)

The king is on c3.  Here are the recent moves:

1. ... Bd5+ (or Bxd5+)

2. c4 bxc3+ (e.p.)

3. Kxc3+

Ah, Shivsky beat me to it since I had some work to take care of before I could take a good look at it.

How in God's name can you tell where that King was!? 

It does not matter where the white king is placed the game is a draw. It would be on c3 and white takes the black rook next move

The logic goes something like this:

We notice that it is black to move.  Either he is in check, or the white king is on b3 or c2.  The white king can not be on c2 because kings can't mutually check each other.  The white king can not be on b3 because otherwise white would be in check during black's move.  Thus, the black king is in check.

Now we go back a move.  What move did white make to create this check?  It couldn't have been a move with the bishop because the only places the bishop could come from are the same line that causes the check (in other words, black would be in check on white's move).  If the bishop didn't move, then since the king is the only other piece, it must have been a king move uncovering the check from the bishop.

This means that the king was previously on either b3 or c2.  It could not have been on c2 on that move for the same reason that it can't be on c2 now.  Thus, the white king must have been on b3 and then moved somewhere to uncover the check.  A quick check of the possible moves the white king has from b3 and we see there are only two places it could move that would not leave it in check: a3 and c3.  On which of these two squares is the king, now?

Here is where you have to start thinking a little outside of the box.  On b3, the king is in an impossible double check.  There is no move black could have made to create it with just the pieces on the board.  However, this doesn't mean that there couldn't have been a piece on the board that the white king captured in order to uncover the check.  Recall, however, that the king had to have moved to either a3 or c3 to uncover the check on the black king.  We have to think of a move - either with the rook, the bishop, or some as yet undetermined piece on a3 or c3 - which creates the unique checking situation we see.  It couldn't have been a move with the rook or bishop, for the same reason that we determined we need the extra piece. 

So, we need a move from a piece to a3 or c3 that uncovers both the rook's line to the king and the bishops line to the king.  Since these are distinctly different lines, with no common point except the square the white king was on at the time, we see that a normal move or a normal capture would not have done it.  However, an en passant capture is unique in that in it, a piece is captured on a square it is not currently on.  Trying this out, we see that such a capture on c3 does uncover both the rook's line to the king as well as the bishop's.  Thus, we can move back a couple more moves, since en passant captures must be done with specific timing - leading to the full answer given by both Shivsky and myself.

I agree with the answer, given the above position, but I am not able to understand the position. How is it possible to arrive at the given position with the two pawns using rational thinking, such that the black rook is under attack with the white bishop having no space to move. Also, what did white move instead of capturing the rook such that the next move from black is a check using bishop ?