They followed him from the home where they traced suspected bombers, he was wearing a coat on a summer day where the temp was nearing 80 degrees, he jumped over a police barricade and refused to stop when warned several times. Seems to me the police don't need much more reason. BTW, they now know that he was there on an expired visa - probably the reason why he ran. He is responsible for his actions which resulted in his death.
...He is responsible for his actions which resulted in his death...
The question remains, if the police belived that he were a suicide bomber, why they let him on a crowded place like an underground station, they could challenge him or wound him on more quiet streets from that house to the underground...