It’s both surprising, and not, if you think about it. The way I’ve usually seen it happen is first the rear tire goes flat, then the front one. My theory is that both tires went through the same pile of glass/thorns/metal bits and they both picked up junk. the reason for the flat occurring on the back first is because there’s more weight on that tire, so the offending article works its way through the tread more quickly.
Brakes come in a variety of designs depending on the age and style of your bike. Rim brakes offer more modulation but have less stopping power, so are more suited to riding on the roads. Disc brakes can provide huge amounts of stopping power so are best suited to off road riding, although ‘V’ rim brakes are also well suited to mountain biking. All brakes use a friction system to stop the movement of the wheel, so regular checks of the contact pads should form part of your regular cycle maintenance.