The Jewish comedian David Baddiel used a pithy Facebook post to dismantle Ken Livingstone's bizarre claim – for which the former London mayor was suspended by Labour – that Adolf Hitler supported Zionism "before he went mad and ended up killing six million Jews".

Livingstone had his suspension extended by a year, taking the total penalty to two years, after an investigation into his comments by a Labour party committee. His many critics in the party were hoping for his expulsion and accused him of anti-Semitism.

The hard-left Labour veteran is facing a fresh probe, this time by Labour's ruling National Executive Committee, over comments made more recently. The first investigation only covered his original claims, but he has since repeatedly defended what he said as based in historical fact.

The original Livingstone thesis, made in an LBC Radio interview with Vanessa Feltz, was eyebrow-raising to say the least.

"Let's remember, when Hitler won his election in 1932, his policy then was that Jews should be moved to Israel," Livingstone said. "He was supporting Zionism – this before he went mad and ended up killing 6 million Jews."

Now David Baddiel has taken it to pieces in this must-read post on his Facebook page.