Have there been examples in history where a police force has been converted to a military force? If so, when and why?

The Japan Self-Defense Forces were once, and still technically are, a police unit.

After the end of the second world war, Japan was rapidly demilitarized by the allied (primary US) occupation authorities. The organizational bureaucracy of the pre-war Imperial Japanese Military was disbanded, firearms were collected and destroyed, and any organization associated with military or martial skills was banned. Even the teaching of traditional Japanese Martial arts was outlawed, and the manufacture of Katana was was made illegal. By 1946, Japan was probably the least militaristic society in the world.

For a nation with such a long martial history, the Japanese put up surprisingly little protest to dismantlement. Much has been written on the subject by greater writers than I (Dower's "Embracing Defeat" is a particularly good overview), but suffice to say pacifism rapidly became a central idea in Japanese culture and politics. In 1947 the new Japanese constitution formalized this. As part of Article 9, Japan formally renounced war as a tool of public policy and agreed to never maintain "land, sea, and air forces, as well as other war potential".

Pronouncements like these meant little to Japan's many criminal gangs, of course. Out of work and disenfranchised, many former soldiers were fell into lives of crime. Allied soldiers were ill-equipped to navigate the complex cultural issues involved with local law enforcement, so domestic police forces were quickly re-established after the occupation began.

For a time, this is how Japan functioned. Native Japanese police handled local issues, and the allied military handled issues of national significance. But in 1950 North Korea invaded the South, sparking a 3 year conflict that would cost millions of lives. The US was caught totally off guard by this move. After years of post war draw-downs, the US Army was dangerously short of men. To fight off the invading North Koreans, they redeployed virtually every allied solider in Japan to the Korean peninsula.

That Japanese were understandably rather alarmed at the prospect of being utterly undefended while such a massive war raged a short sea crossing away. With the cooperation of the allied authorities the formed a 75,000 man "National Police Reserve". Armed with light infantry weapons, this group would go on to form the nucleus of today's Japan Self-Defense Forces. Also established was the waterborne Coastal Safety Force, a small green water navy.

In 1952 the allied occupation of Japan formally ended. Also in that year the National Police Reserve and the Coastal Safety Force were compined into the National Safety Forces. The new force was also expanded to 110,000 men. In 1954 it's forces were separated out into the Ground, Air, and Maritime Self Defense forces we see today.

As part of it's unique legacy, members of the Self Defense Forces' legal status is unlike that most militaries. They are considered civilians, and can resign at any time. This causes all sorts of retention issues, which have continually plagued the JSDF since its foundation.

I hope than answers your question!