How cdk/cloudformation understand which subnet is PRIVATE OR PUBLIC?

I have three subnets in AWS.

One is public because it has internet-gateway

And other two are not.

However when cdk synth, there comes template cdk.context.json

It judges every three subnets are Public

However other two are Isolated in fact(without NAT gateway and public IP)

Why cdk think they are Public??

  "vpc-provider:account=678100XXXXXX:filter.vpc-id=vpc-0867d6797e62dd78b:region=ap-northeast-1:returnAsymmetricSubnets=true": {
    "vpcId": "vpc-0867d6797e62dd78b",
    "vpcCidrBlock": "10.0.0.0/24",
    "availabilityZones": [],
    "subnetGroups": [
      {
        "name": "Public",
        "type": "Public",
        "subnets": [
          {
            "subnetId": "subnet-0b5985476dee1f20c",
            "cidr": "10.0.0.0/25",
            "availabilityZone": "ap-northeast-1c",
            "routeTableId": "rtb-02a749d8d4415bbfb"
          },
          {
            "subnetId": "subnet-0fdd37150bfff91f0",
            "cidr": "10.0.0.128/26",
            "availabilityZone": "ap-northeast-1c",
            "routeTableId": "rtb-02a749d8d4415bbfb"
          },
          {
            "subnetId": "subnet-085c85398f27adbfd",
            "cidr": "10.0.0.192/26",
            "availabilityZone": "ap-northeast-1d",
            "routeTableId": "rtb-02a749d8d4415bbfb"
          }
        ]
      }
    ]
  }
}