MARIUPOL, Ukraine—Ruslan Abalmaz, a martial-arts enthusiast with intricate tattoos running down his arms, spent seven years in jail on extortion charges. He's now a police officer, a switch that would have seemed laughable to him just months ago.

"It's a paradox," Mr. Abalmaz said as he raced a green-and-black van filled with men carrying automatic weapons through the streets of this seaside town, on their way to battle with pro-Russia insurgents.

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