Deadlock in Cluedo is possible

Yesterday when we played Cluedo and all almost simultaneously came to the final conclusion (if I got it correctly, me, Zingis and Marina got the solution first, while Liene and Sergejs at least partly came to it from our behaviour), the game turned into a run for the room where you should make the accusation and win the game (as it is the room where the murder was committed). However each of us was too far to reach the room in one turn, so when anyone would come closer to the entrance of THE MURDER ROOM some other player would simply call the fastest runner to some other room. So nobody could win the game and we decided to end it in a draw. Actually I had never thought before that an outcome like this could be possible in this game.